During a loss of coolant accident (LOCA), timely and accurate detection of the break size is crucial for nuclear power plant safety. However, current methods rely on the personal judgment of operators, which fail to meet the requirements of both speed and accuracy in high-risk situations. In this study, a CNN-LSTM model is proposed to detect the break size of LOCA, with six optimization algorithms used to tune the model hyperparameters. The GWO-WOA optimized model achieves the lowest validation loss (0.1563) and standard deviation (0.01462), outperforming the unoptimized model. To enhance model interpretability, SHapley Additive exPlanations (SHAP) analysis was conducted. Its results align with actual accident analysis, indicating that the model effectively captured the key features of the accident and enhanced the operators' trust in the AI model. Furthermore, three SHAP-based feature selection strategies were analyzed to reduce the number of required features and improve model performance. The results show that the selection strategy based on the mean SHAP value, which reduces the test set MSE from 0.196 (original feature combination) to 0.0396, is closest to the optimal feature combination. These findings offer practical guidance for developing LOCA break size detection systems, enhancing accident response timeliness and effectiveness.

To efficiently simulate the localized three-dimensional transient response of nuclear power systems, a semiimplicit iterative coupling method combining FLUENT and NUSOL-SYS has been developed using a domain decomposition approach. The method derives coupling boundary pressure corrections by analyzing the impact of pressure changes on mass flowrates and iteratively adjusts boundary pressures to achieve mass flowrate balance and convergence. After verifying the accuracy of the derived pressure correction in relation to mass flow rate and the stability of the coupling under varying time steps, coupling simulations of parallel channel flow demonstrate its accuracy. Finally, a comparative analysis using the TALL-3D test facility confirms that the coupling simulation results are in close agreement with standalone NUSOL-SYS calculations. This method provides a non-intrusive semi-implicit coupling strategy for decomposed domains in nuclear reactor systems, based on pressure correction derived from an analytical approach to the fluid computation domain.

Due to the nearly solid core and passive heat removal characteristics, the heat pipe cooled reactor (HPR) exhibits considerable potential for self-stabilization and self-regulation under load-variation condition. The U-50Zr metallic fuel, with its high structural strength and excellent thermal diffusivity, is expected to further enhance this capability. Therefore, during the load-variation condition, the optimization and characteristic analysis of the heat pipe reactor core with U-50Zr metallic fuel (U-50Zr MHPR core) are studied. Firstly, the transient analysis code is developed, with validation performed against experimental data of the load-variation condition of KRUSTY. Then, the transient response of the highest power density design scheme is analyzed to determinate of the evaluation metrics. To improve computational efficiency, a method combining neural networks and transfer-learning is adopted. By splitting and fusing the network architecture, knowledge from a high-accuracy steady-state surrogate model is transferred to a corresponding branch of the surrogate model for load-variation conditions, enabling high prediction accuracy even with a limited number of samples. Guided by three proposed evaluation metrics and the hybrid decision making method CRITIC-TOPSIS, a core design with strong self-stabilization and self-regulation capabilities is subsequently selected, featuring an enrichment of 61.93% and a core power density of 10.71 kW L−1. Finally, the optimized core is coupled with an open Brayton cycle system, and its transient characteristic under load-variation and abnormal conditions are analyzed. Under the ±5% load-variation condition, by the system's internal feedback mechanisms, a new steady-state is reached within 1520 s. In the abnormal operating condition where the inlet air temperature drops to 228.15K and the performance of the heat pipe decreases by 30%, the thermal-hydraulic parameters remain within the safe limit. This study can serve as a reference for the optimization of the U-50Zr MHPR core with enhanced self-stabilization and self-regulation capabilities.

Coupled simulations of system and CFD codes are essential techniques in numerical reactor research. This coupling approach combines the advantages of both codes, enabling high-precision and rapid simulations across multiple scales. It meets the needs of global effect analysis while accurately capturing critical details, thereby providing precise support for reactor design optimization and safety assessments. This study develops a semi-implicit pressure correction iterative coupling method based on domain decomposition, using the commercial computational fluid dynamics software FLUENT and the system analysis code NUSOL-SYS. In this method, a consistent initial pressure value is set at the coupling boundary. The boundary pressure is then adjusted step by step to establish a sensitivity relationship matrix between pressure and mass flow rate. Additionally, the velocity difference across the boundary at each iteration step is used to calculate the coupling pressure correction. Throughout the iterative process, the coupling boundary pressure is continuously adjusted to ensure that the velocities on both sides converge, achieving overall convergence. After verifying the stability of the coupling method through a parallel flow problem, this computational tool is applied to analyze the core inlet flow distribution of the modular small pressurized water reactor ACP100 under a primary coolant pump trip accident. The results show that the system parameters of the coupled code align with the standalone calculations of NUSOL-SYS, while also being capable of simulating local three-dimensional flow phenomena. The proposed method provides valuable reference for multi-scale simulations in the thermal–hydraulic analysis of nuclear power systems.

This study develops and applies transient and steady-state one-dimensional–three-dimensional (1D–3D) heat transfer coupling methods for the simulation of helically coiled steam generators in high-temperature gas-cooled reactors (HTGRs). In this framework, the 1D system code NUSOL-SYS models the fluid and heat structures inside the helically coiled tubes, while the 3D CFD solver FLUENT simulates the shell-side helium flow. Bidirectional data exchange is implemented at the coupling boundaries, enabling coordinated iterations of wall temperature and heat flux between the tube-side and shell-side. The accuracy of the shell-side CFD model is verified against the Žukauskas correlation. Time step constraints for transient coupling were derived and validated, and recommended under-relaxation factors for steady-state coupling are established. Coupling simulations are performed for both a local 1/20-length three-layer helically coiled and a full-length five-layer helically coiled tube model. Results show that the steady-state coupling yields predictions consistent with the transient simulation, while requiring only 5% of the computational cost. For the full-scale model, the coupled simulation predicts outlet temperatures deviate by less than 5.02% from the actual reactor values. The proposed multi-scale 1D–3D coupling methodology provides an efficient and accurate tool for analyzing complex flow and heat transfer phenomena in HTGR steam generators, offering valuable guidance for design optimization and performance evaluation.

In nuclear engineering applications, processes such as inverse uncertainty quantification critically rely on surrogate models capable of accurate and efficient uncertainty estimation. Traditional uncertainty-aware regression models, such as Bayesian Neural Networks, make distributional assumptions that often diverge from real-world system behavior, and are associated with high computational costs. To address these limitations, a deterministic neural network method, Softmax-based Deep Neural Network (Softmax-DNN), is proposed. It reformulates real-valued regression tasks into classification problems and employs the Softmax activation function to construct an uncertainty-aware regression model. Without assuming a specific output distribution, Softmax-DNN directly predicts the probability density function through a single forward pass, enabling efficient and flexible uncertainty estimation. The hyperparameters and overall performance of the model were evaluated using three numerical experiments and two practical thermal-hydraulic problems. Comparing Softmax-DNN to Bayesian Neural Networks, Monte Carlo Dropout, Deep Ensemble, and Gaussian Process shows that it not only achieves prediction accuracy comparable to other neural networks but also provides more reliable uncertainty intervals for the predictions. Furthermore, Softmax-DNN significantly reduces training and inference time due to its deterministic structure and relatively simple architecture. Overall, the proposed Softmax-DNN provides an accurate, assumption-free, and computationally efficient surrogate model approach with uncertainty estimation in complex nuclear systems.

[Background]In the digitalization and digital twin construction of Lead-cooled Fast Reactors(LFRs),the efficient prediction of the temperature field in heat exchangers is a key technical link to ensure the safe operation and optimal control of reactors.Among the various heat-exchanger configurations,the supercritical carbon dioxide(SCO2)helical-coil heat exchanger is considered one of the promising options for application in LFR.However,although full-scale Computational Fluid Dynamics(CFD)can elaborate on the heat transfer and flow mechanisms of spiral tube heat exchangers in detail,it incurs high computational costs and is difficult to meet real-time requirements.[Purpose]This study aims to propose a Proper Orthogonal Decomposition(POD)-Artificial Neural Network(ANN)framework based on a non-intrusive reduced-order method for enhancing the efficiency of reduced-order prediction of temperature field for LBE-SCO2 helical tube heat exchanger.[Methods]Firstly,the high-fidelity CFD data was utilized to extract typical modes and modal coefficients via POD,and establish a nonlinear mapping relationship between inlet flow velocities and modal coefficients with the help of an ANN.Then,model validation and grid-independence verification were conducted,and the temperature field was rapidly reconstructed on the basis of POD-ANN framework.Finally,prediction results were compared with that of the full-order CFD simulations.[Results]Comparison results show that the computational efficiency of the proposed model is improved by more than five orders of magnitude compared with full-order CFD simulations,and the average relative errors of temperature field prediction for both the tube side and shell side are below 0.2%.[Conclusions]Results of this study demonstrate that the model significantly enhances computational efficiency while maintaining high prediction accuracy,providing robust support for the design optimization of heat exchangers and the digital twin applications of LFRs.

The Best Estimation Plus Uncertainty Analysis (BEPU) method has become an important method for accident analysis and safety review of nuclear power plants. One important aspect of this method is to quantify the uncertainty of the Thermal-Hydraulics (T-H) codes. In some models, such as reflood models, the experimental data are often time-series data, which presents a challenge for traditional uncertainty quantification methods. To address the limitations of the traditional Bayesian calibration method, an improved approach was developed by integrating functional data analysis (FDA), principal component analysis (PCA), the Affine-Invariant Ensemble Sampler (AIES) Markov Chain Monte Carlo method, and the hierarchical Bayesian method. The UCB reflood experiment was used to evaluate the performance of the enhanced method in quantifying uncertainties and to propagate the quantified input uncertainty to the cladding temperature output. The results show that the functional data analysis method helps select quantities of interest in sensitivity analysis. The principal component analysis method can effectively improve computational efficiency and the envelopment of the posterior propagation results relative to experimental data. The Affine-Invariant Ensemble Sampler method can reduce calculation time. The hierarchical Bayesian method can effectively improve the envelopment, but it will significantly reduce the computational efficiency. The combination of principal component analysis with hierarchical Bayesian allows for the greatest possible envelopment of experimental data.

A compact megawatt nuclear power system, which couples a heat pipe cooled reactor with a supercritical CO2 Brayton cycle (named SUPERHERO system), has been proposed as a power source for large unmanned undersea vehicles (UUVs). The operational performance of UUVs is directly affected by the regulation capability of the system's output power. Consequently, in order to enhance the load-following capability of the SUPERHERO system, the characteristics of the system at different load-following rates are analyzed in this study, and then the optimization directions for the original control system are proposed. One direction is that the traditional Proportional-Integral-Derivative (PID) controllers are replaced with the BP neural network PID controllers to enhance the system's load-following capability by coupling the developed transient analysis code with the MATLAB/SIMULINK platform. Another direction is that the target values of the control parameters are optimized to enhance the load-following capability. Firstly, the impact of the target values of the control parameters on the load variation capabilities is analyzed, and then the optimization parameters and objectives are determined. Based on the Non-dominated Sorting Genetic Algorithm II (NSGA-II), the optimal target values of the control parameters are obtained, and the system's load-following rate is successfully increased to 18.4 % of full power per minute. Subsequently, based on the optimized control system, the transient characteristics of the system are also analyzed under the scenario of a single control system failure. The results show that the special attention should be paid to the variation rate of the turbine inlet temperature and the failure of the compressor throttle valve.

Heat pipe cooled reactors have been developed more than 60 years, primarily utilizing ceramic fuels such as UO2 and UN. However, the inherent characteristics of ceramic fuels impose limitations on the power density improvement of the heat pipe reactor core. In response to this challenge, an innovative conceptual design of a heat pipe reactor core with U-50Zr metallic fuel is proposed in this study. When addressing the multi-objective, multi-parameter and multi-physics coupling design challenges of heat pipe reactor cores, it is essential to introduce an efficient design and optimization method based on data-driven multi-physics coupling and multi- objective optimization analysis. Therefore, a three-dimensional multi-physics coupling analysis code is developed employing Matlab, OpenMC, and COMSOL. To enhance computational efficiency, the neural network surrogate models are established to replace the original code. Additionally, NSGA-II is utilized to obtain the optimal core design schemes, focusing on the objectives of higher power density of the core and lower fuel enrichment. Finally, in the results of the Pareto front, the detailed multi-physics coupling analyses are studied on two different core design schemes characterized by lower fuel enrichment and higher power density of the core, respectively. The design scheme with high power density features lower peak temperatures and lower peak stresses. In contrast, the design scheme with low enrichment provides a more uniform power distribution and greater backup reactivity. Both design schemes satisfy the operational requirements for a ten-year lifecycle, with temperatures and stresses remaining within the safety limits. This demonstrates the effectiveness of the proposed design approach and the analytical code. This study provides a reference for the design and multi-objective optimization of the heat pipe reactor core with U-50Zr metallic fuel and establishes a foundation for future transient optimization efforts.

Accurate prediction of the temperature distribution within the fuel-heat pipe assemblies is crucial for the design optimization and safety analysis of heat pipe reactors. A Physics-Informed Neural Network (PINN) model is proposed for rapid prediction of the temperature fields in fuel-heat pipe assemblies under varying boundary conditions. The effects of various loss functions (MSE, MAE, Huber Loss) and sampling point numbers on the model performance were investigated. Among these, the MSE demonstrates the best performance, achieving an average relative error of 0.114 %. Furthermore, increasing the sampling points can improve the prediction accuracy, with the training time increasing sublinearly due to parallel computation. In order to improve the model performance, three model types (purely data-driven, purely physics-driven, and hybrid-driven) were analyzed. The results showed that the average relative error of the hybrid-driven model is the lowest at 0.09763 %. In order to improve the model prediction performance and training speed under target domain shifts, transfer learning method was introduced. For the purely data-driven model trained with only ten cases, transfer learning reduces the average relative error from 8.031 % to 0.4107 %. The hybrid-driven model also benefits from transfer learning, decreasing the average relative error from 0.1179 % to 0.08879 %. This study demonstrates the effectiveness of the PINN in temperature field prediction for engineering applications.

Nuclear Thermal Propulsion (NTP) offers significant advances over conventional chemical propulsion systems, providing high thrust, high specific impulse, long endurance and reusability. These capabilities are well suited to the increasing requirements of future space missions. This study focused on the medium-thrust, solid-state, closed-cycle NTP engine, selecting nine critical design parameters for a comprehensive multi-objective optimization (MOO) analysis based on three steady-state performance metrics by implementing the Non-dominated Sorting Genetic Algorithm III (NSGA-III) algorithm and coupling the SCTRAN code to calculate the steadystate thermal-hydraulic parameters. The results presented a range of optimal engine configurations. For scenarios with two predefined mission objectives, the study recommends optimal values for a third performance objective in addition to the nine most important system design parameters. The optimal designs showed a reduced global sensitivity for certain parameters, thereby increasing the robustness of the system. The reliability of the optimization approach was confirmed by comparing one of the study's detailed steady-state results with existing literature. The paper concluded with key optimization recommendations that are instructive for future NTP engine design and refinement.

The heat pipe-cooled reactor is an ideal power source for unmanned underwater vehicles (UUVs) due to its compact design, simple structure, and high safety features. However, a heat sink loss accident may lead to reactor damage, requiring a passive residual heat removal system (PRHRS) for emergency cooling. This study presents a novel compact heat pipe reactor with a PRHRS that uses natural circulation to cool the heat pipes' adiabatic sections. A steady-state CFD simulation optimized the geometry, and a transient analysis code was developed in FORTRAN and validated with CFD results. The findings show a sharp increase in fuel temperature immediately after the accident, followed by a decrease as natural circulation cools the reactor. Throughout the accident, component temperatures stayed within permissible limits, with the maximum fuel and heat pipe temperatures not exceeding 965.13 K and 972.5 K, respectively. No boiling occurred in the PRHRS cooling water. This confirms that the PRHRS effectively removes residual heat, ensuring reactor safety during both steady-state and accident conditions, and lays the groundwork for the design of new MW-class compact heat pipe reactors.

To meet the flexible and reliable power supply requirements of specialized scenarios, such as deep space and deep-sea exploration, a novel megawatt nuclear power system that couples a heat pipe cooled reactor with a supercritical CO2 Brayton cycle was proposed. During the early stages of system design, the start-up process represents a critical transient condition that had to be carefully considered. Optimizing the start-up strategy is vital for improving system flexibility and safety. Traditional approaches, which often rely on manual tuning and empirical adjustments, are inefficient and frequently fail to provide an optimal start-up strategy. This underscores the need for a systematic approach to start-up optimization. In this study, the Sobol sensitivity analysis method was initially applied to evaluate the influence of relevant control input parameters on performance and start-up duration. After identifying the critical input parameters, a database was generated using a system analysis code developed by our team. A surrogate model was then built using a backpropagation neural network. Subsequently, a genetic algorithm was employed to derive the optimal start-up strategy based on the surrogate model. The results demonstrate that, constrained by the heat pipe limit, loop flowrate stability, and a temperature ramp rate below 10 K/min, the system start-up time was significantly reduced to 17,955 s compared to the original strategy of 33,452 s. This outcome effectively enhances the system's flexibility and overall design efficiency, showcasing the superiority of the proposed optimization approach.

Data-driven fault diagnosis has attracted much attention in the field of nuclear energy. The complex operating environment of nuclear power plants tends to cause data to deviate from its own source domain, resulting in domain discrepancy thus performance degradation. So it is crucial to study the performance of the model under domain discrepancy. In this study, two evaluation metrics are proposed for domain discrepancy namely the generalization ability to fault severity and the robustness to data failures. Commonly used fault diagnosis models are built based on ACP100 reactor model, including simple Recurrent Neural Network (RNN), Long Short-Term Memory(LSTM), and Convolutional Neural Networks(CNN). The performance variations of these models are analyzed under the above domain discrepancy. The effect of noise is also analyzed in order to simulate real-world operations. In addition, the model performance is improved by Artificial Disturbance Methods, and the effects of different levels of model noise are analyzed. The LSTM model performs better than the other two models, according to the results under domain discrepancy. The maximum performance gain occurs when 10 dB of noise is introduced. These results provide a reference for the establishment and improvement of future fault diagnosis models for nuclear power plants.

The heat pipe cooled reactor presents a competitive power source for unmanned underwater vehicles (UUVs), which differs significantly from traditional reactors, and conventional residual heat removal methods are not well-suited for the specific operational requirements of heat pipe cooled reactors. Therefore, based on a conceptual design for an underwater nuclear power plant called the SUPERHERO (SUPERcritical carbon dioxide cycleHEat pipe ReactOr power system), a passive residual heat removal system (PRHRS) tailored for the heat pipe cooled reactors used in underwater scenarios is designed in this study. The PRHRS utilizes the space between the evaporation and condensation section of the heat pipe bundle (namely the emergency cooling section) to set up an emergency cooling chamber (ECC). Coolant is filled into the ECC, with the heat pipe bundle serving as the heat source and seawater as the heat sink, forming a natural circulation system that continuously extracts heat from the core. Numerical simulations indicated that with an axial length of 160 mm for the ECC, the PRHRS can conservatively achieve a maximum heat removal power of 0.14 MW. Additionally, experimental research was conducted to study the variation characteristics of the heat removal power and the axial wall temperature distribution of the heat pipe, focusing on variations in coolant mass flow rate, coolant temperature, and heat pipe operating temperature. The experimental results indicated that heat removal power exhibits a logarithmic correlation with coolant mass flow rate, a linear negative correlation with coolant temperature, and a linear correlation with heat pipe wall temperature. The wall temperature of the emergency cooling section significantly decreased compared to steady-state, and variations in coolant mass flow rate and temperature have minor effects on the heat pipe wall temperature. This study provides insights into the design of heat pipe cooled reactors intended for UUV.

The prediction of criticality excursion in fuel solution system has a significant impact on criticality safety analysis. The behavior of radiolytic gas bubbles, which may be influenced by inertial pressure, is crucial for the progression of criticality excursions. A two-dimensional model is proposed to calculating the bubble growth in order to simulate power and pressure in fuel solution system. The model is verified with experiments conducted at the SILENE facility and the influence of inertial pressure on radiolytic gas bubbles is analyzed by comparing the calculation results with and without the consideration of pressure changes. The comparison results indicate that pressure initially slows down the rate of power decline, while it speeds up the rate of power decline in the later stage of power decrease. Neglecting the pressure change during fast pulse transients may leads to a significant underestimation of the energy in the first burst. However, as the maximum inverse period of those experiments decreases, this underestimation becomes less significant and may even be overestimated slightly in turn.

Background A megawatt-class nuclear power system has been developed by coupling a heat pipe reactor with a supercritical carbon dioxide (S-CO2) Brayton cycle. This system offers advantages in terms of high safety, power density, and compactness. Purpose This study aims at the operation characteristics of this power system with high efficiency and compactness. Methods The coupling code of a self-developed heat pipe reactor transient analysis code, Transient Analysis code for heat Pipe and AMTEC power conversion space Reactor power System (TAPIRS), and supercritical carbon dioxide Brayton cycle transient analysis code (SCTRAN/CO2) were utilized to analyze the open-loop dynamic characteristics under conditions of reactivity disturbance, load disturbance, cooling water temperature disturbance, and cooling water mass flowrate disturbance. Then, the control system was designed. On this basis, three load variation operation conditions, i.e., linear load variation, stepped load variation, and load rejection, were simulated and analyzed. Results The simulation results show that the rotational speed of the new nuclear power system is sensitive to the disturbances and needs to be controlled. The bypass flowrate increases under low load conditions, hence the flowrate of the compressor needs to be controlled as well. The system can adjust the load from 0% to 100% at a rate of 6% FP (full power)·min-1. It is capable of implementing stepped load changes, although it experiences slightly more pronounced fluctuations. Under load rejection conditions, the stabilization time might be prolonged, but it will eventually stabilize with all parameters remaining within safe limits. Conclusions This study provides a reference for the conceptual design of new nuclear power systems with high efficiency and compactness.

The new megawatt nuclear power system coupling a heat pipe cooled reactor with a supercritical CO2 Brayton cycle is considered one of the most promising energy conversion systems for large Unmanned Undersea Vehicles (UUVs). This system combines the characteristics of a heat pipe cooled reactor and a S-CO2 Brayton cycle, such as heat pipe start-up limitations and significant thermal inertia. It is unclear whether existing start-up control strategies for either heat pipe cooled reactors or S-CO2 Brayton cycle are suitable for this new system. Therefore, the start-up characteristics and the control strategies of the new megawatt nuclear power system are investigated in this study. A simulation code is developed for the study of the start-up characteristics of this system, which includes models for the reactor, heat pipes, and the S-CO2 Brayton cycle. The validation of the code is conducted based on the experiments as well as the design values. Good agreement between the calculation results and the experimental values or the design values are obtained. And then, the control scheme and start-up strategy of the new system are proposed. The start-up process is divided into four sub-stages, that is, core start-up from cold to critical state, heat pipes start-up, compressor start-up and turbine preheating, and branch switching. Different control strategies are applied to each sub-stage. The results show that the shaft raising rate of 2000 rpm/min is effective in overcoming expansion resistance without causing excessive overshoot in mass flowrate. This control strategy can achieve stable start-up of the new system without exceeding a temperature change rate of 10 K/min. This research may serve as a reference for the conceptual design of this new megawatt nuclear power system.

Heat pipe cooled reactors (HPRs) have been considered as one of the most promising candidates for deep space and deep-sea missions due to their advantages of simple structure, high power density and high reliability, etc. To investigate the transient characteristics of such heat pipe cooled reactors, including startup, shutdown, power transients and accident conditions, it is necessary to develop suitable and efficient models for describing the core, the heat pipe and the power conversion system. Especially, for the startup process, an accurate and efficient model for the simulation of high-temperature heat pipe startup from the frozen state is indispensable. In this study, two transient models based on the dusty gas model (DGM) were developed. The first model (model 1) solved the mass and momentum equations of vapor flow, while the second model (model 2) simplified the vapor flow as a 1D steady-state heat conduction problem using an equivalent network model. The models considered the evaporation/condensation flux at the vapor/liquid interface using the kinetic theory of gases. The wick and wall were modeled using an improved network model, which took into account the phase transition of the working fluid in the wick. Different methods were used to solve these models in this paper. For the model considering the vapor flow, the finite-difference discretization scheme and the SIMPLEC algorithm were used to solve the governing equations. For the equivalent network model, a loosely coupled numerical method is employed. The solution of wick and wall equations was in a transient state, while the equivalent heat conduction equation of the vapor flow was solved in a steady state mode. The alternating direction implicit (ADI) was adopted to solve the equations for the wick and wall regions. The startup experiments of high-temperature heat pipes with different working fluids are simulated to validate the accuracy of these models. The results indicate that the simulation results agree well with the experimental data. Compared with the flat-front startup model, the temperature distribution calculated by model 2 is more accurate, and the description of startup is more plausible. Meanwhile, model 2 gives quite reasonable results although it is less accurate than the model 1. The calculation efficiency of the model 2 is significantly improved compared to model 1. Consequently, in the feasibility study stage of an HPR system, the simplified equivalent network model (model 2) with considering both accuracy and efficiency is suitable for the simulation of heat pipe startup.