Critical heat flux prediction is a core issue in nuclear reactor safety and thermal-hydraulic design. Traditional empirical correlations often only work within narrow ranges, and most machine learning models—though powerful—remain black boxes with limited physical interpretability, which makes engineers hesitant to trust them in practice. To find a middle ground, this study applies symbolic regression via the PySR algorithm to develop an interpretable CHF prediction framework. Instead of fitting a black-box model, the method automatically searches for explicit mathematical expressions that relate key thermal-hydraulic parameters to CHF, producing formulas that are both compact and physically meaningful. Using a database of over 20,000 experimental data points, the resulting models show strong performance. The best candidate achieves a mean absolute percentage error of 11.56%, which is fairly close to the LUT(9.68%) and clearly better than most conventional correlations. We also tested robustness by adding noise to the inputs, and the expressions remained stable. Further parameter sensitivity analysis showed that the optimal model’s expression aligns with known physical mechanisms identified in previous research, reinforcing its interpretability and credibility. Overall, symbolic regression offers a practical compromise between purely empirical correlations and uninterpretable machine learning—delivering accurate, transparent, and reliable CHF predictions for thermal-hydraulic applications.

Understanding bubble behavior is an important issue on boiling phenomena. Bubbles exhibit distinct motion characteristics and morphological changes under different heating surface orientation conditions, thereby influencing the heat transfer coefficient and critical heat flux (CHF). However, compared with the vertical or upward situations, studies on the heating surface facing downward are relatively rare. In order to efficiently capture bubble information and conduct the evolution analysis of bubble boiling, this study develops a bubble recognition method based on an artificial intelligence algorithm YOLOv8, applying to obtain the bubbles information from a nucleate boiling experiment with the downward-facing heater surface. The videos under different mass flux and heat flux are captured by high-speed cameras, including the bottom and the side of the flow. In previous studies, bubbles were mostly assumed to be spherical. In actual situations, especially in downward-facing heater surface, bubbles tend to compress during their growth. Based on a presumed ellipsoidal bubble model, velocity, radius, growth rate and shape change of bubbles were analyzed. The result shows that bubbles are sliding and growing at uniform speed in the experiment. Two key parameters' distributions were proposed and measured, constructing a model for the change in bubble radius and volume. This result provides assistance for further research and engineering design, such as CFD of bubbles, construction of boiling heat transfer models, and design of reactor safety systems.

The long-term performance evolution and fission gas release (FGR) behavior of liquid metal-cooled fast reactor (LMFR) fuel elements are crucial for reactor safety and radioactive source term assessment. In this paper, to address the deficiencies of fuel performance analysis models for LMFR, a multi-physics field-coupled fuel performance analysis program is developed by using the FAST and CAMPUS program architectures and integrating the key physics models of FEAST, KMC-fuel, and other fast reactor programs. The program contains core modules for thermal-physical analysis, FGR, and chemical element migration (oxygen/plutonium), and considers a joint oxide gain (JOG) formation module. The program adopts two-dimensional axisymmetric geometry modeling to enhance the computational efficiency. Based on the verification of the program simulation results in comparison with the irradiated data of the experimental reactor, the present model shows high accuracy in the prediction of fuel temperature field distribution, gap closure kinetics, and fission gas release share (average relative error with experimental data is significantly lower than that of the FEAST model), and that the overall program is able to simulate the evolution of the overall performance of the fuel element well. Based on the validation of the overall performance of the program, the study also analyzes the key role of line power and JOG formation on fuel performance. It is shown that the pellet thermodynamic temperature rises significantly with increasing fuel operating power, which exacerbates the FGR behavior and induces an increase in cladding stress. More critically, the formation of JOG enhances the thermal conductivity of the fuel gap, which changes the temperature field distribution of the pellet, the mechanical deformation of the material, etc., and is thus a key factor that should not be ignored in the process of accurately predicting the change in fuel performance.

This study numerically investigates the temperature and thermal stress fluctuations on a solid plate surface induced by coaxial-jet flow. A one-way fluid-structure coupling approach is adopted, combining Large Eddy Simulation (LES) for the fluid domain with Finite Element Analysis (FEA) for the solid plate. The numerical model is validated through grid and time-step independence studies, showing good agreement with experimental temperature data. Based on the validated model, parametric studies are conducted to examine the effects of plate height and cold-to-hot jet velocity ratio on the transient thermal stress characteristics. The results indicate that the thermal stress distribution on the plate surface is lower in the central region and higher toward the periphery, with higher stress levels occurring in areas impinged by the hot jet. The dominant fluctuation frequencies of thermal stress are below 4 Hz, with peaks near 0.6 Hz and 1.4 Hz. The fluctuation amplitude attenuates rapidly with increasing depth into the plate. As the plate height increases, the surface-averaged stress first decreases and then increases, while the maximum stress decreases monotonically; the fluctuation intensity also shows a nonmonotonic trend. Regarding velocity ratio effects, thermal stress levels are higher when the cold-to-hot velocity ratio is less than 1, and lower when it exceeds 1. However, the case with a velocity ratio equal to 1 exhibits the strongest fluctuation intensity. This work provides insight into the thermal stress fluctuation behavior induced by coaxial jets and offers a reference for thermal fatigue assessment in nuclear power systems and related engineering applications.

In the event of a severe reactor accident, leaked radionuclides can mix with gas. After passing through the coolant pool, they may spread within the reactor system, posing a serious threat to reactor safety. Thus, conducting mechanistic calculations on the capture of radionuclides in mixed-gas bubbles by coolant pools is crucial for ensuring the safe operation of reactors. This paper focuses on evaluating the application of diverse models in water-cooled reactors (WCRs) and sodium-cooled fast reactors (SFRs). The four main models include SASS (Semiempirical model for the Aerosol Scrubbing in a Sodium coolant pool), SPARC-90 (Source Term Program for Analysis of Reactor Containment - 90), I-COSTA (In-Containment Source Term Analysis) and POWERS. As a comprehensive model, SASS can reflect the reality well in the simulation of both WCR and SFR. The other three models have serious distortion of results in calculating the scrubbing process of SFR pools, but they still satisfy the trend of consistency with experimental results in the sensitivity analysis of key experimental parameters. In subsequent research, it was discovered that the fundamental logic underlying the consideration of aerosol pool scrubbing removal is remarkably similar in both the WCR pool scrubbing model and the SFR pool scrubbing model. This finding not only provides a theoretical foundation but also offers valuable inspiration for the development of pool scrubbing models for lead-bismuth-cooled fast reactors.

Lagrangian meshfree particle methods are well suited for simulating free-surface flowsinvolving large deformation and complex interface motion. However, their computationalcost becomes significant for highly viscous fluids because explicit time integration suffersfrom diffusion-number restrictions, whereas implicit schemes require repeated solutions oflarge-scale linear systems and pressure equations. To address this issue, this study proposesa discretized momentum-equation-constrained physics-informed Graph Network-basedSimulator (PI-GNS) framework for accelerating meshfree particle simulations.The training data are generated using theMoving Particle Hydrodynamics (MPH) method,and the particle system is represented as a graph, where particles correspond to nodes andneighboring particle interactions correspond to edges. Unlike the original purely data-drivenGNS, PI-GNS incorporates a physics-informed loss based on the discretized momentum equation.Specifically, the network predicts particle acceleration and pressure increments, whilegraph-based differential operators are used to evaluate the pressure-gradient and viscousdiffusionterms on the particle graph. The discrepancy between the GNS-predicted accelerationand the acceleration evaluated from the discretized governing equation is penalizedduring training.The method is applied to fundamental free-surface flow problems, including dam-breakand box-drop simulations, under different fluid viscosities. The results show that PI-GNSimproves the prediction accuracy of particle displacement and pressure compared with theoriginal GNS, regardless of the geometrical complexity and fluid viscosity. The results alsoshow that the pressure field predicted by the PI-GNS is smoother than that obtained fromthe original particle simulation.The proposed PI-GNS also substantially accelerates the simulations, achieving up to a530-fold speed-up over GPU-based computation in the highest-viscosity cases. To assess theextrapolation capability, an untrained flow condition, namely a dam-break problem with a small obstacle and the dam-break problem in a computational domain twice as large as thetraining dataset, is predicted using the trained model. Although small discrepancies remain,PI-GNS demonstrates significantly improved extrapolation capability compared with theoriginal GNS, whose rollout prediction becomes extremely unstable. These results indicatethat the momentum-equation-constrained PI-GNS provides an accurate, stable, and efficientsurrogate framework for highly viscous meshfree particle simulations.

We present a Moving Particle Hydrodynamics (MPH) solver for granular flows that couples a fully Lagrangian formulation with an elastoplastic constitutive law. Stresses are advanced using the Jaumann objective rate; plastic strain follows a standard flow rule; yielding is governed by the Drucker-Prager criterion. The governing equations are discretized via MPH particle-interaction models and integrated explicitly to update stress, velocity, and position. The method is validated against three benchmarks: (i) static granular dam-break with uniform grains, (ii) large-scale landslide, and (iii) jet impingement and packing in a rectangular container. In dam-break tests, simulations reproduced the angle of repose sharply and exposed internal stress fields inaccessible to measurement; spreading-length discrepancies suggest that tuning Young's modulus and Poisson's ratio-used here as calibration parameters-can further improve accuracy, with angles of repose within +20 % of measurements. Landslide simulations captured overall behavior across particle-size ranges and aspect ratios; agreement was strongest for finer grains, while deviations at smaller nominal sizes likely reflect unmodeled packing-fraction effects that reduce effective bulk friction. In the impingement-packing case, the computed bed shape and repose angles matched experiment and DEM, with angles within +10 %. These results indicate that elastoplastic MPH provides a practical, scalable alternative to DEM for large-deformation, size-heterogeneous granular flows.

Nucleate boiling plays a pivotal role in the in-vessel retention (IVR) strategy of nuclear reactors, as it directly impacts the cooling of molten core materials. This paper presents a comprehensive review of the existing research in this area. Numerous experiments have been conducted to investigate various factors that influence the critical heat flux (CHF), such as gap size, inclination angle, oxidation, irradiation, and coolant types. In addition, innovative methods, including the utilization of nanofluids, nanostructures, and honeycomb structures, have been developed to enhance the CHF. However, there are significant discrepancies between the experimental conditions and the actual IVR applications. These discrepancies encompass differences in equipment, fluid properties, and environmental variables. To address these gaps, it is essential to develop more realistic experimental setups, accurate models, and conduct in-depth applied research. Such endeavors will significantly enhance the reliability and safety of IVR strategies, thereby making a substantial contribution to the overall safety of nuclear power plants.

Accurately predicting fission gas release (FGR) in light water reactors (LWRs) is crucial for ensuring nuclear fuel integrity and reactor safety. This study developed and validated a machine learning framework to predict FGR behavior in LWRs fuel using a high-fidelity dataset generated by the CAMPUS multi-physics code. Four AI models—including Transformer, Mamba, Random Forest (RF), and Ridge Regression (RR)—are trained and evaluated on the dataset. Through hyperparameter optimization and systematic input parameter combination analysis, we identify the optimal configurations for each model. The results show that the Transformer and Mamba deep learning models demonstrate excellent predictive performance and generalization ability, while the RF outperforms others on training data but lacks extrapolation ability seen in deep learning models. Furthermore, a controlled-variable analysis is conducted to explore the individual influence of six key input parameters on FGR, revealing physical insights into the relationships between operating conditions and gas release behavior. This work not only confirms the feasibility and effectiveness of AI models in FGR prediction but also provides a practical methodological foundation for future applications in nuclear fuel performance assessment and safety margin evaluation.

Fuel-coolant interaction is a complex multiphase multicomponent mass and heat transfer phenomenon encountered in many industrial settings. During severe accidents of light water reactors, thermal and hydraulic interactions play a considerable role in the fuel-coolant interaction. Aiming to further clarify the fragmentation behavior of molten fuel in water, we carried out a set of experiments by injecting molten copper jets (serving as a simulant of molten fuel) into a water tank. By adjusting parameters covering melt temperature, water temperature, melt penetration velocity, and water depth, the effects of these parameters on the fragmentation behavior of molten copper jet are systematically investigated. Experimental results indicate that under higher water temperatures, molten copper cannot solidify and instead remains in liquid form, reaching the water tank bottom. This leads to the formation of large agglomerates. As the melt temperature increases, the fragmentation products become larger, with a denser fragment bed and more spherical particles. Higher penetration velocity of the molten metal results in smaller particles. However, it doesn't significantly affect debris bed porosity and debris sphericity. Large aggregates are formed at shallow water depths. While debris bed porosity remains nearly constant, deeper water tends to yield fragments with higher sphericity. Weber number theory performs better in predicting the mass median diameter of debris formed, compared with other fragmentation models. This article provides some experimental results that contribute to supporting the development and validation of light water reactor safety analysis codes in China.

Space thermionic nuclear reactor (STNR) has the characteristics of large delay and strong nonlinearity. It is difficult to obtain the satisfied performance with traditional control system. Model prediction control (MPC) is adopted in this study. The control law is designed and optimized through the prediction model and objective performance function. The problem of poor control performance of large delay system is solved and fast regulation is achieved. The model predictive controllers are designed at different power levels. Gain scheduling method is utilized to improve the tracking accuracy of the nonlinear system. This approach enables stable operation of STNRs across the full-power range. It is shown from the simulation analysis under the representative operational scenarios that the model predictive control system based on gain scheduling has smaller overshoot and settling time than the traditional control system. The fluctuations of major parameters are reduced significantly. Therefore, the proposed gain scheduling model predictive control provides a promising strategy to the control of STNR.

In this paper, we propose an innovative artificial intelligence (AI) -based method to estimate drag coefficients in two-phase flows by predicting void fraction. To solve the problem of the limited application range of traditional empirical relationships, four AI models, namely random forest, Transformer, Mamba and ridge regression, are used in this study to train and predict horizontal gas-liquid two-phase flow void fraction database (6554 data points). By analyzing the influence of input parameter combination, it is found that liquid velocity plays a key role in reducing the prediction error, and the optimal parameter combination is pipe diameter to length ratio, pressure and liquid velocity. The results show that the random forest model has the best performance, with a mean error (ME) is only 1.32 %. Further research has shown that the Transformer model has high accuracy in evaluating the effects of a single parameter. Finally, the high accuracy of random forest in estimation of drag coefficient is verified by the correlation formula between void fraction and drag coefficient. This study reveals the potential of AI model in the prediction of complex two-phase flow parameters, and provides a new idea for intelligent prediction of drag coefficient.

Nucleate boiling effectively dissipates heat through phase change, where heat is absorbed during the transition from liquid to vapor. However, this heat dissipation is strongly limited by Critical Heat Flux (CHF). When CHF is reached, a small increase in heat flux can lead to a sudden temperature surge, potentially causing the heated surface to burn out. CHF has been extensively studied for almost 100 years, and numerous methods have been proposed to predict CHF under various working conditions. In this paper, we aim to comprehensively review the methods for predicting CHF, from initial models derived from experimental correlations to advanced numerical simulations and state-of-the-art machine learning approaches. We begin by introducing CHF models based on experimental data and discuss prediction methods that utilize CHF databases. Next, we examine wall boiling models developed through numerical simulations at different scales. Furthermore, we explore the potential of machine learning in CHF prediction, highlighting the advantages of this approach. By summarizing these studies, we aim to provide researchers with a comprehensive understanding of CHF prediction methods and offer effective strategies for accurate CHF prediction in the future.

Understanding fluid-structure interaction is essential across many engineering applications. This work presents a fully explicit Lagrangian-Lagrangian solver based on the Moving Particle Hydrodynamics method that treats fluids and structures within a unified analytical framework. A weakly compressible fluid model and a hyperelastic structural model are combined, and the coupling is achieved with a fluid-structure acceleration-based approach that enforces consistent momentum exchange at the interface. Verification and validation include the two-dimensional Turek-Hron benchmarks and three-dimensional dam-break simulations involving elastic obstacles. The solver reproduces structural oscillations, free-surface evolution, and stress distributions in close agreement with analytical references, experimental measurements, and results from established fluid-structure interaction solvers. Complex behaviors such as splash formation and large elastic deformations are captured without ad hoc stabilization. A scalability study demonstrates efficient use of graphics processing units for simulations up to twelve million particles, while reduced efficiency appears for very small particle counts due to memory-allocation overhead. Overall, the solver exhibits physical consistency, strong scalability for large-scale problems, and robustness in highly nonlinear conditions. These capabilities make it a practical, parameter-free tool for high-fidelity prediction in nuclear safety, structural impact assessment, and free-surface flow problems.

Molten metal spreading and solidification behaviors are crucial phenomena in various fields. This study employs Spearman's rank correlation to identify the key parameters influencing spreading behaviors through a series of experiments and Monte Carlo simulations. The experiments utilized three different low melting point alloys, systematically varying parameters such as water level, subcooling, superheating, and jet velocity, among others. The results revealed that the spreading behaviors can be classified into three distinct modes: (1) clear spreading, (2) irregular spreading, and (3) clear sedimentation. These modes are determined by the energy balance between jet inertia and solidification. Dimensionless analyses were conducted to investigate the spread areas and thicknesses. The findings demonstrated that thickness increases exponentially with decreasing the dimensionless volume while the spread area decreases due to enhanced cooling efficiency. Additionally, an empirical dimensionless correlations were developed to predict the spread area and thickness based on the interplay between jet-driven inertial forces and solidification. This correlation indicates that the transition between spreading and sedimentation occurs within a threshold range of 0.1 to 0.3. This threshold corresponds to the solid fraction at which the melt immobilizes as the dynamic viscosity sharply increases due to cooling. Finally, Monte Carlo simulations, utilizing a combination of random sampling and Bayesian modeling, were employed to estimate Spearman's rank correlation. The analysis revealed that the critical parameters for spreading are the latent heat of fusion and the superheat of the melt, as these factors significantly impact the melt's ability to maintain fluidity. In contrast, the melting temperature and subcooling were found to predominantly influence sedimentation by accelerating solidification and enhancing cooling efficiency. These results underscore an empirical correlation that is broadly applicable to general melt spreading phenomena, providing a quantitative framework for identifying the key parameters that govern the process.

In this study, the effect of gap size and inclination angles on the Critical Heat Flux (CHF) on bare copper surfaces is investigated in the context of vertical-facing saturated pool boiling. The research endeavor aims to unravel the intricate relationships between these variables and their collective impact on CHF. Through hypothesis formulation and analysis of the collected experimental data, it has been determined that the effects of the two variables, inclination angle and gap size, on CHF are approximately relatively independent. Based on previous research, experimental data has validated the conclusions that CHF increases with both increasing inclination angle and gap size. Furthermore, an empirical formula has been developed that closely aligns with experimental data, incorporating both contemporary experimental findings and established theoretical models. Comparison with previous data and models has shown that it fits well with the derived formula. The author argues that both variables-inclination angle and gap size-have a significant impact on CHF by modulating the Bubble Film Departure Frequency (BFDF) and the average width of bubbles formed during the boiling process. However, these two variables do not directly affect CHF, instead, they influence CHF by affecting bubble behavior. Bubble behavior is the direct factor in the occurrence of CHF, while gap size and inclination angle are indirect factors. Through analyzing bubble behavior, we can gain a better understanding of how gap size and inclination angle influence the average bubble width and BDFM, as well as how the average bubble width and BDFM affect CHF. This research offers reference for IVR strategy implementation: the In-vessel Corium Retention (IVR) strategy, crucial for mitigating core meltdown accidents, ensures the reactor pressure vessel (RPV) lower head remains intact during severe incidents. The Critical Heat Flux (CHF) on the RPV lower head surface is the main barrier to IVR. Consequently, CHF research is essential for IVR application. While there's extensive research on heating surface inclination and gap size effects on CHF, less focuses on bubble behavior. Instead, they influence CHF by affecting bubble behavior. Bubble behavior is the direct factor in the occurrence of CHF, while gap size and inclination angle are indirect factors. Through analyzing bubble behavior, we can gain a better understanding of how gap size and inclination angle influence the average bubble width and BDFM, as well as how the average bubble width and BDFM affect CHF.

This paper advances our understanding of boiling dynamics at the Critical Heat Flux (CHF) level within a downward flow boiling scenario. Building on initial visual observations, this study clarifies the mechanisms driving CHF front motion and introduces a model to track its progression. It reveals that the CHF front advances when the evaporation rate in the microlayer surpasses the liquid inflow. This insight has facilitated further modeling of the relationship between the CHF threshold and CHF front velocity using a balance model in the microlayer. We observe an inverse yet linear relationship where the ratios Rm/S0 - the microlayer radius to its thickness - and UX - the mean liquid inflow rate - show negligible variation despite changes in surface roughness and flow rates. Additionally, we have refined our CHF prediction model to incorporate effects of surface roughness and flow rate, linking it with the CHF front velocity model. This model, which balances three velocity terms at the CHF front, demonstrates substantial predictive accuracy and suggests that enhancements to the CHF threshold improve rewetting flow, thereby delaying surface dry-out, reducing CHF front velocity and enhancing CHF performance. These findings provide crucial insights for advancing thermal management technologies.