Free-piston Stirling engines offer high theoretical efficiency but involve complex multi-physics instability. Conventional data-driven models focus solely on regression and ignore physical boundaries. This causes optimization algorithms to converge toward physically unfeasible optima, leading to mechanical collisions. This study proposes a physics-aware, multi-stage deep learning framework for robust thermal-fluid analysis. The methodology integrates classification-regression-constraint mechanisms based on a validated third-order nonlinear physical model. Initial screening of 5011 points reveals a 14% steady-state validity rate. An ensemble boosted tree classifier identifies stability boundaries with a 91.14% recall rate. Optimized Gaussian Process Regression models accurately predict the output power (R2 = 0.9811). Meanwhile, a dedicated amplitude model (R2 = 0.9036, RMSE = 0.8775 mm) acts as a reliable soft-constraint penalty to bound piston displacement. This synergistic AI architecture eliminates physical failure risks during global searches. The AIoptimized design achieves a stable 126.44 W electrical output. This represents a 43.6% improvement over the 88 W baseline with a 1.64% prediction error. The system maintains a safe 12.5 mm amplitude against the 16.0 mm physical limit. This threshold provides a statistically robust buffer of 4.0 times the model RMSE. A 1000-sample Monte Carlo analysis under 1% random perturbations confirms high engineering robustness. The primary innovation lies in embedding strict physical-fluid boundary constraints into deep learning networks. This architectural synergy overcomes the inherent limitations of purely data-driven mapping by grounding the learning process in physical reality. It provides a reliable methodology for safely designing tightly constrained oscillating thermal systems.

High-temperature heat pipes,as highly efficient and passive phase-change heat transfer devices,play an irreplaceable role in nuclear reactor core cooling,spacecraft thermal management,and advanced energy systems.One of the key factors limiting their heat transfer performance lies in the capillary driving force and liquid-phase transport capability of the wick structure.Conventional wick designs suffer from an inherent trade-off between capillary pressure and permeability,which constrains the performance of high-temperature heat pipes under extreme heat fluxes and complex operating conditions.In recent years,nanostructure modification technologies have provided new pathways to overcome this bottleneck.This review systematically summarizes the research progress on high-temperature heat pipes with nanostructured wicks,covering the full research chain from microstructural fabrication and characterization,evaporation heat transfer mechanisms of alkali metals,macroscopic heat transfer performance experiments,to multiscale numerical simulations.Studies indicate that nanoscale structures constructed on wick surfaces via methods such as oxidation-reduction and sol-gel processing can simultaneously and significantly enhance capillary pressure and permeability,effectively reducing the thermal resistance of the evaporating meniscus.As a result,the startup speed,isothermal performance,and heat transfer limit of heat pipes can be improved by approximately 10%～40%.Molecular dynamics and lattice Boltzmann simulations reveal the critical influence of surface wettability on liquid sodium evaporation dynamics and flow spreading behavior,and experimentally correlated relationships for the contact angle as functions of temperature and pressure have been obtained.Moreover,multiscale numerical models based on computational fluid dynamics have been developed to predict the transient response and limiting behavior of heat pipes,further validating the heat transfer enhancement mechanisms induced by nanostructures.Finally,experimental studies on the adaptability of nanostructured-wick high-temperature heat pipes under complex operating conditions such as bending,motion,and thermal mismatch,are summarized,and future research challenges and development trends are discussed,including liquid metal flow and heat transfer mechanisms,the effects of non-condensable gases,strong transient and impact responses,high-fidelity code development,and data-driven predictive methodologies.This review aims to provide systematic theoretical insights and technical guidance for the design and application of next-generation high-performance high-temperature heat pipes.

This study proposes an innovative reactor configuration termed the Liquid Metal Matrix-Based Heat Pipe-Cooled Reactor (LM-HPR). The design aims to address two primary challenges in advanced reactor systems: eliminating the additional solid-solid contact thermal resistance between solid matrix materials and high-temperature heat pipe (HTHP) surfaces, and concurrently mitigating the high-temperature dynamic corrosion issues commonly associated with lead-bismuth fast reactors. The heat transfer performance of this novel configuration was investigated using a dedicated lead-bismuth/heat pipe heat exchange prototype (LBE-HPHE Prototype). A specialized experimental platform was constructed to measure critical physical parameters of both the HTHPs and the Lead-Bismuth Eutectic (LBE), facilitating a detailed examination of the heat exchange dynamics between these two media. Initial tests conducted on potassium HTHPs successfully verified stable startup characteristics and excellent isothermal performance. A series of five steady-state experiments were performed under varying LBE temperature conditions. During the final testing phase, the HTHPs exhibited an average axial temperature gradient of 43.82 degrees C and demonstrated a heat extraction capacity of 2.42 kW from the LBE pool. The average equivalent thermal resistance of the HTHPs was calculated to be 0.0516 K.W-1, indicating good overall heat transfer characteristics alongside their confirmed isothermal performance. The average temperature difference measured between the bottom and top layers of the LBE was 5.90 degrees C. Analysis revealed that as the LBE temperature increased, the interlayer temperature difference initially decreased before subsequently increasing, a trend attributed to the evolving performance characteristics of the HTHPs under different operational conditions. With increasing LBE temperature, the heat exchange process between the HTHPs and the LBE intensified significantly. The natural convection heat transfer coefficient exhibited a substantial enhancement, rising from 327.32 W/(m(2).degrees C) to 8431.65 W/(m(2).degrees C). This improvement corresponded with increased heat transfer efficiency of the HTHPs and stronger natural convection heat transfer between the LBE and the HTHPs. Consequently, the Nusselt (Nu) number increased, while the Rayleigh (Ra) number also showed a gradual rise accompanying the elevation in LBE temperature. These experimental outcomes validate the fundamental feasibility of the liquid metal matrix-based heat pipe-cooled microreactor concept, providing crucial empirical data to support its further development and potential deployment.

Free-Piston Stirling Generators (FPSGs) are promising power sources for deep space exploration. Accurate simulation is difficult due to strong multi-physics coupling. Second-order models omit fluid inertia. CFD models are computationally expensive for system-wide analysis. This study proposes a third-order fully coupled dynamic model. The model employs a staggered grid method to solve unsteady compressible flow equations integrated with a non-linear alternator. A 100-W class prototype validated the simulation. The predicted operating frequency is 29.4 Hz with a deviation of less than 2%. The indicated power error is 6.0%. The simulation reveals critical microscopic mechanisms. A distinct hysteresis loop with a peak amplitude of 1800 Pa in the dynamic pressure drop curve confirms the significant impact of fluid inertia under high-frequency oscillation. Gas temperatures at the regenerator boundaries exhibit step-like fluctuations. Instantaneous temperature differences between the gas and the solid matrix reach up to 20 K. This behavior underscores severe local thermal non-equilibrium and entropy generation that quasi-steady assumptions fail to capture. Electromechanical coupling analysis shows that electrical impedance mismatch caused the low power output in reference experiments. Optimizing the resonant tuning capacitor to 560.9 mu F minimizes inductive reactance. This adjustment boosts the output electrical power from approximately 24 W to 85 W. This work provides a robust tool for understanding the transient physics and optimizing Stirling engine performance.

With the increasing global demand for environmentally friendly electricity generation, thermoelectric generators have garnered significant attention due to their ability to directly generate electricity from temperature differentials without combustion or moving parts, making them clean and reliable. When combined with nuclear energy, a clean power source, thermoelectric generators can form compact and silent nuclear power systems with high energy density. Therefore, this work proposes the concept of a heat pipe cooled reactor integrated with three-stage segmented thermoelectric generators, named NUSTER. First, the three-stage STEG was geometrically optimized for use in a heat pipe reactor, achieving a conversion efficiency of 15.78% at a hot-side temperature of 1050 K. Next, a multiphysics simulation model integrating neutronic, thermal, and electrical fields was established in COMSOL to analyze the coupled behavior of NUSTER. The results show that NUSTER can achieve an overall conversion efficiency of 12.08%. Finally, safety analyses were performed to assess NUSTER's performance under representative accident scenarios, including thermoelectric circuit failures, reactivity insertion, and heat pipe failures.

High-Temperature Heat Pipes (HTHPs) are widely used due to their excellent thermal performance and passive characteristics. However, their complex frozen startup process presents significant challenges for numerical simulations, particularly regarding efficiency and accuracy. This study introduces a Convolutional Neural Network (CNN) framework to develop an end-to-end model that predicts and analyzes the physical fields of HTHPs based on operating parameters, enabling rapid and accurate predictions of the frozen startup process. A large-scale dataset encompassing various operating conditions was generated through numerical simulations to train the CNN model. Convergence analysis results indicated that a training size of 1.0 and a network depth of 4 layers are the optimal parameters for the model. The CNN model accurately predicted the physical fields, achieving mean absolute errors of 0.41 K for temperature, 5.12 x 10-5 m/s for axial velocity, 3.24 x 10-6 m/s for radial velocity, and 23.53 Pa for pressure. Additionally, the model demonstrated a prediction speed nearly four orders of magnitude faster than traditional Computational Fluid Dynamics (CFD) methods. It also accurately predicted the wall temperature of HTHPs, with a mean absolute error of only 0.47 K. This study highlights the potential of deep learning for advancing HTHP analysis.

High-temperature heat pipes (HTHP) are key passive heat-removal components in heat-pipe-cooled microreactors, where their frozen startup behavior directly governs reactor safety margins. Existing analyses rely on either empirical system codes or computationally expensive CFD, making it difficult to obtain high-fidelity temperature-field predictions for startup assessment, digital-twin-assisted analysis, and rapid design iteration. This study proposes a deep learning approach for predicting temperature field evolution during HTHP frozen startup. Multiple architectures-U-Net, U-Net-LSTM, U-Net-GRU, Fourier Neural Operator (FNO), and implicit UNet enhanced FNO (IU-FNO)-were systematically evaluated for data dependency, noise robustness, and prediction performance. Results show that IU-FNO achieves superior accuracy, with a mean absolute error (MAE) of 0.49 K and root mean squared error (RMSE) of 1.07 K, by capturing both global features and local details of temperature dynamics. Single-step inference completes within milliseconds on a workstation GPU, roughly four orders of magnitude faster than the reference CFD solver. A transfer learning strategy further enhances adaptability across HTHP configurations, reducing training time by over 90% while maintaining high accuracy (MAE 0.57 K, RMSE 0.90 K). This framework provides an efficient surrogate model for HTHP frozen-startup prediction and offers potential support for thermal-state evaluation and reactor design optimization.

This study conducts multi-physics coupling analysis on the NUSTER-100 heat pipe-cooled fast-spectrum reactor (100 kWe output power, 5-year design lifetime). The core employs a square lattice layout, with an operational temperature range of up to 1473.6 K at the fuel center and 1123.15 K at the condenser section of the heat pipes. The heat pipes are designed with a sodium working fluid and Haynes-230 cladding, featuring a diameter of 25 mm and an effective length of 450 mm. For studying the thermal safety characteristics of the heat pipe reactor NUSTER-100, a three-dimensional thermal hydraulic code was developed based on the external coupling method. It is applied to analysis of the steady-state neutron-thermal-mechanical coupling and calculation of the transient thermal safety characteristics of the core. The external coupling interface is developed to realize the steady-state neutron-thermal-mechanical coupling analysis of the core. The neutron-thermal coupling analysis of transient thermal safety characteristic response of heat pipe reactor core is realized by coupling the point reactor kinetics. The influence of the number and location of failed heat pipes on the reactor core was investigated. The results show that the NUSTER-100 core design is reasonable and feasible, and the core operating parameters meet the thermal safety limits under normal working conditions. The failure of heat pipes at different positions of the core has different effects on the core, and the more heat pipes fail, the greater the impact on the core.

The free-piston Stirling generator (FPSG) provides a promising energy conversion solution for space nuclear power systems (SNPS) and deep space exploration. However, intense multiphysics coupling creates an extremely narrow steady-state operable domain. To ensure high-fidelity performance prediction, a third-order transient thermodynamic solver, previously validated against experimental benchmarks, is employed to capture nonlinear gas-solid heat transfer and fluid inertia effects. To overcome the high-dimensional optimization bottleneck, this study proposes a physics-informed active learning multi-objective optimization (AL-MOO) framework. This mechanism enforces strict thermodynamic conservation constraints and eliminates non-physical pseudo-optima frequently encountered in conventional data-driven methods. Macroscopic performance limits within strict safety constraints are precisely determined: maximum power output reaches 158.6 W (14.4% efficiency), and maximum efficiency peaks at 15.0% (114.9 W). Detailed energy flow breakdowns and entropy generation analysis reveal the underlying microscopic dissipation mechanisms. Pursuing maximum power inevitably triggers exponentially growing unsteady viscous hysteresis penalties, severe local thermal non-equilibrium, and regenerator enthalpy leakage. It simultaneously sacrifices impedance matching, causing significant electromagnetic reactive power losses. Monte Carlo analysis further confirms that the optimal design maintains robust performance under small manufacturing tolerances. This study quantifies the inherent competition between thermodynamic work capacity and energy efficiency, providing thermo-physical criteria for next-generation Stirling energy systems in nuclear applications.

Heat pipe-cooled reactors (HPRs) have gained significant attention due to their compact design, passive heat transfer capability, and enhanced inherent safety features. Although numerous HPR designs have demonstrated passive operational characteristics, the design of the residual heat removal system (RHRS) remains a key technical challenge, as it serves as the ultimate heat sink for the entire system, ensuring core safety. This study presents the preliminary design and assessment of the RHRS in NUSTER, a 100 kWe-level HPR optimized for underwater deployment. First, the NUSTER-RHRS is designed as two independent heat removal systems to enhance system safety and redundancy. Then, a comprehensive HPR simulation framework is developed, validated, and utilized to analyze the complete heat transfer pathway from the core to the final heat sink. Steadystate and transient simulations demonstrate that natural circulation alone can sustain core cooling following a single-sided RHRS failure while preserving over 60 % of nominal electrical power output. Additionally, the results reveal that core-matrix temperature feedback mitigates the negative reactivity introduced by fuel temperature reduction, further enhancing the self-regulating safety of HPRs. These findings provide valuable insights for refining RHRS designs in future next-generation HPR applications.

Heat pipe cooled reactors are a recent hotspot of research in energy systems due to their high energy density, simple structure, and inherent safety. These reactors, operating at near 1000K, require high-temperature heat pipes with alkali metals, which freeze under cold conditions, posing start-up challenges. This work proposes a cascaded control method for heat pipe cooled reactors, integrating neutron physics and thermal-hydraulic models into a coupled control framework. The heat pipe model was improved with a wick structure flow model, achieving a relative error below 9.76%. The framework was used to analyze the start-up characteristics of a 100kWe-level reactor. Simulations indicate that the start-up process involves two power peaks and depends heavily on the heat pipes. Activating the energy conversion system quickly is crucial, overcoming an initial control dead zone. A constant start-up rate of 0.01% FP/s extends the start-up time to 12,000 seconds. However, a variable rate strategy, shifting from 0.01% to 0.05% FP/s, reduces this to 5,500 seconds. The steady-state velocity in the central heat pipe wick is approximately 0.0155 m/s with a pressure drop of about 9140 Pa, displaying a trapezoidal velocity profile.

High-temperature alkali metal heat pipes, crucial in energy system heat transfer, are examined for their multi-domain and multi-field complexities, focusing on frozen startup transient analysis. An OpenFOAM-based code was developed, integrating models for startup dynamics, wall heat conduction, wick and vapor space phenomena, and non-condensable gas effects, achieving validation accuracy within 10% relative error. Analysis of a horizontal sodium heat pipe reveals that increased non-condensable gas content accelerates startup and alters temperature distribution. Sensitivity studies show higher inclination angles enhance wick pressure drop. These findings contribute to optimizing high-temperature alkali metal heat pipe design, advancing understanding of their mechanisms and improving energy system performance. This research advances thermal management in energy systems, laying groundwork for innovations in heat pipe technology and enhancing design precision and efficiency.

The global demand for reliable and sustainable energy resources has been growing rapidly, driven by the need for clean and eco-friendly power sources. In response, microreactors are emerging as a promising small-scale nuclear power solution, combining high efficiency, low cost, and reduced risk compared to traditional nuclear power plants. With modular and scalable configurations, microreactors are ideal for meeting the energy needs of remote locations, such as islands, mining sites, and military bases, as well as supporting critical infrastructure systems, hospitals, and essential services. Compared to traditional commercial nuclear power plants, small modular reactors (SMRs) are nuclear power systems with a generating capacity below 300 MW, according to the technical report by the International Atomic Energy Agency. Microreactors, a type of SMR, are small portable devices used to provide up to 20 MW of electricity to microgrids or off-grid objects. These devices can be transported via spacecraft, ships, or trucks, as they can be loaded into containers.

Heat pipe-cooled reactors are attractive because of their compact structure, high power capacity and reliability, and inherent safety features. These reactors are distinguished by the use of high-temperature heat pipes that directly bridge the reactor core and energy conversion devices, thus creating a tightly knit modular system. However, comprehensive coupled analysis of these reactors remains challenging because of the intricate multiphysics interactions involved. To address this, the neutronic and thermoelectric coupled phenomena of heat pipe-cooled reactors are investigated in this study. Models are introduced for the point reactor kinetics, core heat transfer, channel heat transfer, two-phase two-dimensional heat pipes, thermoelectric coupling, and cold plates. The channel heat transfer is refined in a 100 kWe-level nuclear silent heat pipe-cooled reactor and a model for the three-dimensional heat transfer process in its thermoelectric matrix established, which effectively resolves the calculation distortions of the lumped model. The maximum deviation between the calculation results from the proposed model and the verification data for a full-system coupled computation is less than 10 K. The core temperature difference from the three-dimensional model is five times that of the lumped model with a maximum average fuel temperature difference of 225.7 K. The maximum and average thermoelectric conversion efficiencies are 15.56 % and 14.43 %, respectively. The failures of one, five, and nine heat pipes are analysed. The failure of a single heat pipe has negligible effects with a peak fuel temperature surge of only 121 K. In contrast, a failure involving nine heat pipes leads to a peak fuel temperature spike of 778 K and a 47.1 % increase in the maximum heat transfer power, marking a critical operational threshold. It is therefore imperative to consider the safety margin in the potential failure of multiple central heat pipes during the preliminary design stages.

In recent years,heat pipe has been widely used as an efficient heat transfer equipment in fuel chemistry,electronic communication and so on.The main structure of a heat pipe mainly includes the vacuum tube containing alkali metal working fluid and the composite mesh wick on the inner wall of the tube.In the axial direction,heat pipes are generally divided into three parts:evaporation section,adiabatic section and conden-sation section.Heat is input into the heat pipe through the evaporation section and output through the condensation section.The adiabatic section only plays a role in connecting and mass transfer.The length of each area can be flexibly arranged.In the radial direction,heat pipes are generally divided into outer wall surface,wick and vapor area.Alkali metal high-temperature heat pipes show broad application prospects in the nuclear reactor cooling and other aspects because of their strong heat transfer capacity and inherent safety at high temperature.Because the working fluid of these heat pipes is solid at room temperature,and whose saturated vapor pressure relatively low,their frozen start-up has a complex phase change process of the working fluid,so it brings some difficulties to the study of the frozen start-up of the high-temperature heat pipes.For different application scenarios,it is necessary to study the transient and steady-state operating characteristics of high-temperature heat pipes,to provide support for the application of high-temperature heat pipes in a variety of applicable scenarios.To estab-lish a method for predicting the transient start-up and steady-state operation characteris-tics of alkali metal high-temperature heat pipes,this study utilized the finite volume method(FVM)to establish the pipe wall heat conduction model,the wick flow heat transfer model,and the vapor zone model.A frozen start-up transient analysis program for alkali metal high-temperature heat pipes was developed and verified using the C programming language,with a maximum relative deviation of 9.8％.Transient start-up of a single horizontal sodium heat pipe was simulated,and sensitivity analysis was conducted.The steam zone of the heat pipe enters the continuous flow state completely 700 seconds after start-up,and after a total of 3 000 seconds,the heat pipe reaches steady-state operation.Under steady-state operation,the heat pipe exhibits good iso-thermal properties,with a stable axial temperature difference of 22.5 K on the outer wall and an internal pressure drop of approximately 47 Pa in the wick.Furthermore,the ambient temperature primarily impacts the time required for the heat pipe to reach stead-y-state,as well as the vapor pressure and velocity distribution under steady-state condi-tions.Meanwhile,the length of the adiabatic section of the heat pipe influences the time required for it to reach steady-state and has a significant effect on the pressure and velocity distribution of the wick.

Heat pipe cooled reactor is one of the most popular types of reactor for power users who need high-density and reliable energy source because of its exclusive properties such as compacted structure, flexible layout and “none-liquid coolant”. In the design and selection of micro or small marine nuclear power system, especially the 100-kw marine nuclear power system, heat pipe reactor can perfectly meet the requirements of high power density and strict volume and weight constraints [1]. However, since there is a lack of domestic and foreign mature design technical specification systems and typical mature models or prototype for reference, it’s hard to design the full-scope proto of this type of nuclear reactor [2]. This paper introduces a nuclear power reactor design verification platform developed based on simulation platform that can support the simulation of full scope of marine heat pipe reactor. Through the integration of system-level design and analysis codes, coupling simulation of multiple systems models, automatic generation of models of heat pipe as well as fuel arrangement matrix and radial heat transfer calculation, the platform implements a method not only for the rapid full-scope heat pipe nuclear reactor system modeling establishment but also for the real-time calculation of the steady-state or transient simulation, which lays a numerical calculation foundation for the design and verification of heat pipe nuclear reactor system.

Heat Pipe cooled Reactor (HPR) has the advantages of compact structure, high power capacity, high reliability, and inherent safety. It is often considered to have no loss of flow or loss of coolant accident during the heat pipe cooled reactor operation, because there is no flowing coolant working across the major equipment (the coolant only evaporates, condenses and transfers inside the heat pipe) and the working pressure is low. However, due to the limitations of the thermo-physical properties of the fluids inside the tube and the structure of the wick, the heat pipe has an inherent working temperature range, and the heat flux at the hot end is likely to change sharply which could result in the failure of the heat pipe. While the heat pipes are closely arranged in the reactor, an abnormal operation of a single heat pipe may lead to the continuous failure of multiple heat pipes around it in a short time. Thus, the impact of such accidents on the operation safety and reactor reliability should be considered in the heat pipe nuclear reactor design and safety analysis. This paper provides a system-level simulation scheme to analyze the possible consequences of such kind of accident in a rectangular heat pipe reactor. In addition, the important indexes safety margin of the reactor during the transient of heat pipe failure is evaluated and calculated.

Heat pipe cooled reactor (HPR) features high power density, compact structure, long operation life and high reliability, which is an excellent candidate for small nuclear power source for deep space or underwater missions. In this paper, a conceptual Nuclear Silent Thermal-Electrical Reactor (NUSTER) is preliminarily designed, using 109 sodium heat pipes for passive cooling. The thermoelectric generators (TEGs) are employed in the reactor to convert fission heat to electric power. Based on the design, a HEat pipe cooled Advanced Reactor Transient analysis code (HEART) is developed, including point reactor kinetics model, multi-channel model, core heat transfer model, heat pipe model, thermoelectric generator model and coolant model. The models proposed in HEART are preliminarily verified against the design value and experiment data, and the maximum deviation is less than 12.3%. Steady-state performance of the NUSTER are successfully predicted by HEART, and results indicate that the solid-state core has good temperature flattening ability. The surface temperature of the heat pipe is less than 1300K, and the average temperature drop of the TEG module in central channel is 724.1K, which can produce an electrical power of 301.94W. The models developed in HEART can also be applied to other heat pipe cooled reactors, providing valuable experience in design and thermal-hydraulic evaluation of HPRs.