Reactor Core Research Articles

Development of dynamic simulation model for 20 kWe micro heat pipe fission battery with dual power conversion system

Recent advancements in politics, technology, and economics have sparked interest in small-scale nuclear power generation. Heat-pipe micro-reactors, a type of small modular reactor (SMR), are ideal for remote and specialized applications like deep-sea and deep-space exploration. Traditionally, these reactors have used thermoelectric generators (TEGs) or Stirling engines for power conversion. However, TEGs suffer from low efficiency, and while Stirling engines have improved, they still have lower long-term stability compared to TEGs. Furthermore, comprehensive studies on system-level transients, dynamic behavior, and thermal responses are lacking. This study designs and models a dual power conversion system integrating TEGs and Free-Piston Stirling Generators (FPSGs) for micro heat pipe reactors to enhance efficiency, stability, and reliability. By integrating the two systems in parallel, the limitations of each technology are addressed, offering a robust solution for small, portable nuclear power generation. A dynamic simulation model incorporating the reactor core, heat pipes, and power conversion system enabled a comprehensive study of system transients and interactions. The core was modeled using thermal energy balance equations, and a thermal resistance approach was applied to the heat pipe. The TEG model included the Thomson and Seebeck effects, while neutronics feedback used a point kinetics model. The nonlinear analysis model was applied to simulate the FPSG. The system reached a stable operation after about 1000 s, generating 20kWe with 29.39% efficiency. It maintained stability without external control during transients within a specific range, demonstrating its feasibility. The TEG and FPSG exhibited independent yet complementary behaviors, ensuring reliable performance across scenarios.

Steady-state thermal–hydraulic analysis of an NTP reactor core based on the porous medium approach

Nuclear thermal propulsion (NTP) is a promising advanced technology which has attracted wide attention in recent years. The reactor core is an essential component of an NTP system and the corresponding thermal–hydraulic analysis is necessary. In this study, the porous medium approach was applied to the simulation of a two-pass NTP reactor core which consists of the porous prismatic cermet fuel elements. The thermodynamic property models of hydrogen and the fuel element materials were implemented, as well as the empirical correlations of the heat transfer coefficient and the friction factor. The three-dimensional simulation of a single fuel element was carried out and the results were compared against another code. The code-to-code comparison verified the applicability of the porous medium approach. The three-dimensional model of the two-pass NTP reactor core was established and the steady-state simulation was carried out. The distribution patterns of the parameters are determined by the thermal–hydraulic characteristics of the reactor core, including the nonuniform heat release, contact heat conduction and folded-flow scheme. The full-core heat-flow adaptability analysis is realized, which provides a reference for the thermal–hydraulic safety analysis of the NTP reactor.

Potential to Identify the Neutrino Mass Ordering with Reactor Antineutrinos in JUNO

Abstract The Jiangmen Underground Neutrino Observatory (JUNO) is a multi-purpose neutrino experiment under construction in South of China. This paper presents an updated estimate of JUNO's sensitivity to the neutrino mass ordering using the reactor antineutrinos emitted from eight nuclear reactor cores in the Taishan and Yangjiang nuclear power plants. This measurement is planned by studying the fine interference pattern caused by quasi-vacuum oscillations in the oscillated antineutrino spectrum at a baseline of 52.5~km and is completely independent of the CP violating phase and the neutrino mixing angle θ23. The sensitivity is obtained through a joint analysis of JUNO and TAO detectors utilizing the best available knowledge to date about the location and overburden of the JUNO experimental site, the local and global nuclear reactors, the JUNO and TAO detectors responses, the expected event rates and spectra of signal and backgrounds, and the systematic uncertainties of the analysis inputs. It is found that a 3σ median sensitivity to reject the wrong mass ordering hypothesis can be reached with an exposure of about 6.5 years × 26.6~GW thermal power.Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Article funded by SCOAP3 and published under licence by Chinese Physical Society and the Institute of High Energy Physics of the Chinese Academy of Science and the Institute of Modern Physics of the Chinese Academy of Sciences and IOP Publishing Ltd.

On the Use of a Chloride or Fluoride Salt Fuel System in Advanced Molten Salt Reactors, Part 3; Radiation Damage

Structural materials in fast reactors with harsh radiation environments due to high energy neutrons—compared to thermal reactors—potentially suffer from a higher degree of radiation damage. This radiation damage can change the thermophysical and mechanical properties of materials and, as a result, alter their performance and effective lifetime, in some cases leading to their disintegration. These phenomena can jeopardize the safety of fast reactors and thus need to be investigated. In this study, the effect of radiation damage on the vessels of molten salt fast reactors (MSFR) was evaluated based on two fundamental radiation damage parameters: displacement per atom (dpa) and primary knock-on atom (pka). Following the previous part of this article (Parts 1 and 2), an iMAGINE reactor core design (University of Liverpool, UK—chloride-based salt fuel system) and an EVOL reactor core design (CNRS, Grenoble, France, fluoride-based salt fuel system) with stainless steel and nickel-based alloy material vessels, respectively, were considered as case studies. The SPECTER and SPECTRA-PKA codes and a PTRAC card of MCNPX, integrated with a module which has been developed in MATLAB, named PTRIM and SRIM-2013 (using binary collision approximation), were employed individually to calculate and compare dpa and PKA (this master module containing all three tools has been appended to the iMAGINE-3BIC package for future use during reactor operations). Additionally, SRIM-2013 was applied in a 3D simulation of a radiation damage map on a small sample of vessels based on the calculated PKA. Our results showed a higher degree of radiation damage in the iMAGINE vessel compared to the EVOL one, which could be expected due to the harder neutron flux spectrum of the iMAGINE core compared to EVOL. In addition, the nickel alloy vessel showed better radiation damage resistance against high energy neutrons compared to the stainless steel one, although more investigations are required on thermal neutrons and alloy corrosion mechanisms to determine the best material for use in MSFR vessels.

Thermo-neutronic integrated coupling effects on nuclear reactor core calculations

Small Modular Reactors (SMRs) have gained significant attention as the next generation of nuclear reactors due to their unique features, such as improved economic viability and safety. This study focuses on the SMART reactor, the first certified design of an SMR, and investigates various Thermo-Neutronics aspects using an integrated coupling scheme of nuclear codes. The Neutronics cell and core calculations are performed using the DRAGON/DONJON codes, while the COBRA code is employed for thermal-hydraulic calculations. The analysis considers parameters including axial and radial power peaking factors (PPFs), critical heat flux (CHF), minimum departure from nucleate boiling ratio (MDNBR), axial average coolant temperature in hot channel and core, and maximum fuel temperature. These parameters are evaluated using the developed coupling system. Code-to-code verification is conducted to ensure the accuracy of the results, demonstrating good agreement. The coupling approach reveals significant effects compared to stand-alone code modeling, emphasizing the importance of considering the coupling between Neutronics and thermal-hydraulics, especially during the cycle length. This study contributes to the understanding of SMRs, particularly the SMART reactor, by providing insights into key parameters and their interdependencies. The integrated coupling scheme enhances the accuracy of the analysis and highlights the significance of considering coupling effects in the modeling process during the steady state and the cycle length.

An Innovative and Efficient Implementation of Matrix-Free Newton Krylov Method for Neutronics/Thermal-hydraulics Coupling Simulation

The core physical behavior of reactors is essentially the result of multi-physical fields coupling feedback. High-fidelity neutronics/thermal-hydraulics (N/TH) analysis can simulate and predict nuclear reactor core phenomena realistically, providing advanced and reliable technical means during the design and safety analysis of nuclear reactor. In this work, an efficient and robustness coupling method using power density as the coupling parameter, Matrix-Free Newton Krylov (MFNK) method, is successfully developed and innovatively implemented in HNET for high-fidelity N/TH coupling simulation. To enhance the efficiency and stability, the multi-level generalized equivalence theory-based CMFD (ML-gCMFD) iterative acceleration method and ML-gCMFD coupling acceleration method are proposed. In addition, the nonlinear preconditioning and hybrid perturbation size formula are implemented to further improve the convergence. Finally, to evaluate the numerical accuracy, convergence, efficiency and stability of MFNK method, a series of representative problems, including a three-dimensional (3D) single fuel pin problem, VERA Benchmark Problem 6, and VERA Benchmark Problem 7, are analyzed by comparing with the current N/TH coupling methods. Numerical results indicate that MFNK method can obtain strong stability, high convergence performance, and relatively high computational efficiency while ensuring high accuracy. It demonstrates that MFNK method has significant performance advantages and potential for high-fidelity N/TH coupling simulation.

Numerical heat transfer analysis of steam injection into subcooled water

Steam direct contact condensation (DCC) into subcooled water may be encountered in different important industrial process applications, such as steam jet pumps, steam ejectors, pressurizers, and emergency cooling systems of nuclear reactor core. In this work, a numerical simulation study has been done for injection of steam into a tank full of subcooled water. In the simulations, the Eulerian multiphase flow in addition to a realizable k-epsilon turbulence model has been utilized. Moreover, a DCC model has been used for condensation capturing. Fluent software with a user-defined function (UDF) for the DCC model was employed for simulations. The results obtained from simulations were validated with experimental results, and a fair agreement was observed. This study considered the local Nusselt number (LNN) the most suitable parameter for investigating the heat transfer rate (HTR) at the computational cell level. Therefore, the contours of the LNN, its axial distribution, and radial distribution were studied with respect to the inlet pressure of injected steam, temperature of tank water, and location along the axis of the nozzle. The results reveal the fact that the value of the LNN reaches a maximum at the nozzle exit along the axis of the nozzle at 323 K tank water temperature. LNN decreases by increasing or decreasing the tank water temperature beyond 323 K. It is claimed that the heat transfer (HT) study at such a local scale has been conducted for the first time to the best of our knowledge, and it unfolds various crucial facts regarding steam-water interaction.

Novel modified Chernobyl disaster optimizer for controlling DC motor

This article presents the modified Chernobyl disaster optimizer (CDO) method for DC motor control to find the optimal proportional integral derivative (PID) settings. DC motors are widely used machinery. DC motors are also simple to use. The detonation of the Chernobyl nuclear reactor core served as the inspiration for the idea and guiding principles of the CDO. CDO has limitations in the stability of exploration and exploitation areas. This research aims to obtain a new balance of exploration and exploitation. This study suggests incorporating the levy flight and chaotic algorithm (CA) techniques to enhance the CDO method. This study was conducted with the MATLAB/Simulink software. A comparative technique, which included the marine predator algorithm (MPA), golden jackal optimization (GJO), and CDO, was utilized to determine the performance of the MCDO method. According to the study’s findings, the MCDO method’s overshoot value outperformed all other approaches.

Study on the effects of accident-tolerant fuels on the safety of CPR1000 nuclear power plants

Abstract In this paper, CPR1000 Nuclear power plant was taken as the reference unit. According to CPR1000 Probabilistic Safety Analysis (PSA), the Large Break loss of coolant accident (LOCA), Medium Break LOCA, Small Break LOCA, Station Blackout (SBO), Total Loss of Feed water (TLOFW) and Anticipated transient without trip (ATWT) with Loss of Main Feed water (LOMF) were selected as the representative accident scenarios. The house holding deterministic programs LOCUST were used to analyze each of the above selected scenarios for five different accident tolerant fuels (ATF). The effects on accident process, reactor core damage time, system success criteria and personnel response time were analyzed under the above scenarios. The above results for the five ATF materials were compared to those for standard UO2-Zr in the same scenarios, then some useful conclusions were obtained which can be used to support ATF material selection. In the end, based on the deterministic calculations, the effects of different ATF materials on CPR1000 PSA results such as core damage frequency (CDF) were evaluated in detail with traditional PSA software Risk Spectrum. According to the results, ATFs have some advantages on core damage time, success criteria or operators’ action time window. But the CDF was changed little compared to standard UO2-Zr system. Through the studies, it is found the most important thing is that due to the much longer time windows some new plant modifications can be provided to mitigate the accidents which can contribute to the plant safety and decrease risk more.

Reduced basis method for non-symmetric eigenvalue problems: application to the multigroup neutron diffusion equations

In this article, we propose a reduced basis method for parametrized non-symmetric eigenvalue problems arising in the loading pattern optimization of a nuclear core in neutronics. To this end, we derive a posteriori error estimates for the smallest eigenvalue which is assumed to be simple and the associated left and right eigenvectors. The practical computation of these estimators requires the estimation of a constant called prefactor, which we can express as the spectral norm of some operator. We provide some elements of theoretical analysis which illustrate the link between the expression of the prefactor we obtain here and its well-known expression in the case of symmetric eigenvalue problems, either using the notion of numerical range of the operator, or via a perturbative analysis. Lastly, we propose a practical method in order to estimate this prefactor which yields interesting numerical results on actual test cases. We provide detailed numerical simulations on two-dimensional examples including a multigroup neutron diffusion equation.

Application of Lie symmetry to find an analytical solution for reactor point kinetics equation with prompt jump approximation and power feedback

The reactor Point Kinetics Equations (PKE) are simpler zero-dimensional approximation to space dependent dynamical models of nuclear reactor core, that are accurate enough to describe transients in small to medium size fast reactor cores. Even these simplified equations can be solved only by numerical methods, except in a very few restrictive cases, where they are amenable to analytical solution. Symmetry methods using Lie's point symmetry have been shown to be a systematic and powerful tool to solve any given ordinary or partial differential equation. An approximation of the PKE, known as Prompt Jump Approximation (PJA) converts the coupled system of first order ODEs with one delayed-neutron precursor group and power feedback, into a single first order nonlinear ordinary differential equation. In this study, we demonstrate an application of Lie symmetry method for solving the point kinetics equation under PJA. The analytical solution obtained is compared with benchmark numerical solution of PKE with PJA.

Numerical Investigation of Melting in Pressurized Water Reactor Fuel Rod Considering Operational Parameters of the Core

The meltdown of a fuel rod is a severe accident resulting from the overheating of the reactor core. In the present study, a numerical investigation of this process, focusing on the loss of coolant has been conducted. The objective of this study is to conduct a numerical simulation of transient heat conduction and melting at various points within a typical pressurized water reactor fuel rod. In this analysis, heat conduction in the radial direction of a fuel rod, including the UO2 fuel pellet, the gap, and the zircaloy cladding, is investigated. The FRAPCON steady-state code is employed to calculate the operational parameters of the fuel rod. The calculated parameters, such as coolant and fuel temperatures, fission gas fraction, gap heat transfer coefficient, and burnup, are utilized to evaluate and compare the melting phenomena at different time intervals. In the investigation of the phase change in various parts of the pellet and fuel rod, the explicit finite difference (FD) method is utilized with enthalpy instead of temperature-dependent equations. Finally, the temperature history, phase change, and melting map at different points along the radial and axial directions of the fuel rod during coolant loss and heat transfer coefficient reduction are evaluated based on various operating parameters of the core. To enhance the quality of the results, an uncertainty analysis of effective parameters is conducted. According to this analysis, the heat transfer coefficient of the coolant under accident conditions (0.2 ± 5% kWm−2K−1) and the thermal conductivity of the fuel have the most significant impact on the temperature history and melting process. Highlights include the following: 1. The meltdown of a nuclear fuel rod is analyzed under a loss-of-coolant accident. 2. The enthalpy formula is discretized by the explicit FD numerical method. 3. Effective parameters in melting, such as coolant temperature, burnup, and gap heat transfer coefficient, are obtained by FRAPCON. 4. The temperature history, phase changes, and melting map of various radial points within the fuel pellet and cladding along the axial direction of the fuel rod are determined.

A Reduced-Order Model of a Nuclear Power Plant with Thermal Power Dispatch

This paper presents reduced-order modeling of thermal power dispatch (TPD) from a pressurized water reactor (PWR) for providing heat to nearby heat consuming industrial processes that seek to take advantage of nuclear heat to reduce carbon emissions. The reactor model includes the neutronics of the reactor core, thermal–hydraulics of the primary coolant cycle, and a three-lump model of the steam generator (SG). The secondary coolant cycle is represented with quasi-steady state mass and energy balance equations. The secondary cycle consists of a steam extraction system, high-pressure and low-pressure turbines, moisture separator and reheater, high-pressure and low-pressure feedwater heaters, deaerator, feedwater and condensate pumps, and a condenser. The steam produced by the SG is distributed between the turbines and the extraction steam line (XSL) that delivers steam to nearby industrial processes, such as production of clean hydrogen. The reduced-order simulator is verified by comparing predictions with results from separate validated steady-state and transient full-scope PWR simulators for TPD levels between 0% and 70% of the rated reactor power. All simulators indicate that the flow rate of steam in the main steam line and turbine systems decrease with increasing TPD, which causes a reduction in PWR electric power generation. The results are analyzed to assess the impact of TPD on system efficiency and feedwater flow control. Due to the simplicity of the proposed reduced-order model, it can be scaled to represent a PWR of any size with a few parametric changes. In the future, the proposed reduced-order model will be integrated into a power system model in a digital real-time simulator (DRTS) and physical hardware-in-the-loop simulations.

Assessment of nominal and off-nominal parameters of a soluble boron free small modular reactor design

Boric acid is traditionally used for reactivity control in pressurised water reactors. However, it increases the rate at which reactor components corrode. This leads to increased operational radioactive waste produced through neutron-activation of corrosion fragments. During reactor operation, radioactive corrosion product deposits, or so-called crud, accumulate on fuel cladding in regions of high burnup. Boron compounds have been detected in such deposits, and they cause axial-offset anomaly, i.e. deviation in axial power prediction. Accumulation of boron-laden deposits can reduce plant efficiency to about 70 % over time. This work presents the design process and analysis of nominal and off-nominal parameters of a soluble boron-free small modular reactor core. The design, and analyses were carried out using CASMO4e, CMSLINK, and SIMULATE3 codes. In addition, a borated variant of the target boron-free core was designed and used as reference. Equilibrium cycles were achieved for both the reference and the boron-free core. The limiting FΔH during the transition to equilibrium was found to be 1.754 and 1.651 for the reference and boron-free cores. The equilibrium FΔH were found to be 1.624 and 1.57 compared to the design limit of 1.7. The hot zero power MTC for the boron-free core at beginning of cycle was found to be –22.67 pcm/K compared to −3.64 pcm/K for the reference. The removal of boric acid made the MTC coefficients more negative and the FΔH lower compared to the reference. The boron-free core had enough rod-worth for power and isothermal defect counteraction and reactor shut down.

Integrating the deep learning and multi-objective genetic algorithm to the reloading pattern optimization of HPR1000 reactor core

The deep learning and multi-objective genetic algorithm were employed to optimize the fuel reloading pattern for HPR1000, a state-of-the-art nuclear power reactor designed and operated in China, also known as Hualong-1. In this study, the deep-learning algorithm was applied to establish the rapid evaluator for fuel-reloading patterns, for which the random samples between fuel-reloading patterns and corresponding key core parameters were generated by our home-developed nuclear-design code, named Bamboo-C. The advanced machine-learning platform TensorFlow was utilized for the deep-learning model. Then, the multi-objective genetic algorithm was applied to search the optimal fuel-reloading patterns, combined with the rapid evaluator to evaluate the key core parameters in a very short time. The DAKOTA toolkit was employed for optimization using a multi-objective genetic algorithm, for which the cycle length and power-peak factors were selected as the target parameters to establish the fitness function. For verification and application, the above method has been applied to the fuel-reloading optimization for Cycle 2 of HPR1000 operated in China. The optimization pattern results in an extension of the cycle length by about 21 EFPD (Effective Full Power Day), keeping all the key safety parameters satisfying corresponding safety criteria.

Reactor core design with enriched gadolinia burnable absorbers for soluble Boron-Free operation in the innovative SMR

Effective strategies for maintaining reactor reactivity at a consistent level are indispensable to enable soluble boron-free (SBF) operation in innovative small modular reactor (i-SMR) operation. This paper presents a reactor core design tailored for SBF operation in i-SMR, utilizing concentrated gadolinia burnable absorber rods. This investigation evaluates the concentration range of 155,157Gd and its reactivity characteristics, which are crucial for sustaining excess reactivity. The viability of employing enriched 155,157Gd for the i-SMR SBF operation is established through comprehensive analysis and simulations. Moreover, integrating 155,157Gd with integral gadolinia burnable absorber rods enhances the reactivity control and operational adaptability. Leveraging the spatial self-shielding effect of gadolinia extends the reactivity management capabilities and ensures the operational performance of the i-SMR as optimizing the cycle length. Core design considerations encompassing FA configurations and control rod patterns are investigated to ensure safety and performance across the initial and reload cycles. The feasibility of the SBF operation is verified by assessing compliance with the top-tier requirements of the i-SMR, thus underlining its potential for practical implementation.

Neutronic analysis of new generation TVS-2M fuel assemblies in VVER-1000 reactor type

The Russian fuel assembly TVS-2M is a newly proposed fuel configuration that contains gadolinium-oxide at different concentrations mixed with enriched UO2 at different U-235 enrichment values. The purpose of this study is to investigate the neutronic behavior of the Bushehr VVER-1000 reactor core by replacing the current standard Fuel Assemblies (FAs) called TVS with the new generation of TVS-2M FAs. In such manner, the reactor core was simulated under both modes of TVS-2M and TVS FAs arrangement using the WIMS, CITATION, MCNPX, and SuperMC codes in equal terms. Neutronic parameters of the reactor core such as effective multiplication factor, excess reactivity, neutron flux distribution, power peaking factor, and control rod worth are calculated and discussed within a comparative framework of both configurations of FAs; TVS and TVS-2M.

Application of flow and heat transfer network analysis method to the core of a prismatic gas-cooled micro reactor

Application of flow and heat transfer network analysis method to the core of a prismatic gas-cooled micro reactor

COOLING OF CONTROL RODS AND SPECIFICATION OF CRITICAL TEMPERATURES TO JUSTIFY SAFE OPERATION

The paper analyzes the cooling conditions of the control rods in the mixed core of the WWER-1000 reactor containing fuel assemblies of different vendors (TVSA, WFA/RWFA). The coolant heat-up in the guide thimbles due to own energy release in control rod materials and control rod temperatures required to justify safe operation were calculated for the most conservative case, when the core consists only of TVSAs with a standardized guide thimble inlet plug of NCCP. The energy release was obtained using the calculation method for the boron carbide absorber (B4C), dysprosium titanate (Dy2O3·TiO2), control rod cladding (42CrNiMo), water gap between the cladding and the guide thimble and in the guide thimble (zirconium alloy), fully immersed and 70% immersed RCCA 10th control group. The highest calculated energy release will be observed in fully immersed control rods with boron carbide material at the height position corresponding to the zone of maximum neutron fluence and will be 43.8 W/cm3. The maximum energy release of the 70% immersed (from the bottom of the core) 10th control group is 29.4 W/cm3 for fresh B4C. For the condition of the reactor facility at which the temperatures in FA guide thimbles are maximum, for a "fresh" control rod characterized by maximum energy release in the neutron-absorbing material, the maximum coolant heat-up in the guide thimbles does not exceed 28.9 °C, with the maximum coolant heat-up in FAs being 44 °C, and the maximum control rod cladding temperature not exceeding 335.6 °C at a coolant saturation temperature of 345.8 °C, which indicates that there will be no coolant boiling in the guide thimbles under operation. The maximum temperature typical for the central part of the control rod absorber and for the most conservative calculation for a "fresh" absorber is 529.6 °C, which is significantly lower the melting point of boron carbide, which is ~2350 °C. The maximum calculated temperature in the contact zone of the B4C absorber with control rod cladding is 348 °C. The performed calculations and further analysis of the results confirm that during operation of the RCCA control rods with both “fresh” and “burned-up” B4C, there will be no boiling of the coolant and melting of the absorber in the central part of the control rod. This means that the VVER-1000 core with TVSAs and WFAs/RWFAs and the RCCA rods are reliably cooled.

Resolving the BWR Stability Paradox of Space-Dependent Decay Ratios

Noise signals obtained from local power range monitors and average power range monitors are routinely used for extracting stability information for boiling water reactors. The stability parameters of decay ratio (DR) and natural frequency are produced by signal processing algorithms. While theoretically a dynamical system like a reactor core composed of coherently coupled components possesses a unique DR, noise measurements from different detectors have been reported in several published works to produce different DRs, creating the impression that a DR is not unique at a given operating state but rather is space dependent. This paper is an attempt to reconcile theory with measurements and resolve the space-dependent DR paradox that was encountered afresh in the course of designing a new high-fidelity online stability monitor. As such, the issue of space dependence could not be overlooked as attributable to variability within the uncertainty of noise analysis algorithms.