Advanced microreactors exhibit compact geometries, elevated neutron leakage, and pronounced anisotropic scattering. These characteristics necessitate high-fidelity neutron transport methods to accurately resolve core flux distributions. The neutron transport equation, a seven-dimensional integro-differential equation, poses significant computational challenges in numerical solutions. Conventional acceleration techniques, such as coarse mesh finite difference and diffusion-synthesis acceleration, are widely employed to improve the efficiency of neutron transport codes. However, these approaches often require reformulation of the governing equations or introduce substantial approximations, potentially compromising solution accuracy. To address these limitations, this work introduces a scattering matrix decoupling (SMD) method within the iterative solver framework. This method is designed to reduce computational cost and enhance the overall efficiency of the iterative process in the neutron transport equation. The performance of the SMD method is validated against established neutron transport benchmarks: the strong scattering problem, the IAEA PWR, the gadolinium-bearing BWR, and the KUCA reactor. Results indicate that the effective multiplication factor (keff) and neutron flux distributions remain unchanged with or without the application of SMD, confirming the algorithmic correctness of the implementation. Analysis of the benchmark cases reveals that the SMD method accelerates computation by 86.5 %, 43.6 %, 45.3 %, and 71.6 % for the strong scattering problem, the IAEA PWR, the gadolinium-bearing BWR, and the KUCA reactor respectively. Furthermore, the acceleration efficiency scales with problem size, achieving greater speedup in systems with higher degrees of freedom.

The rapid development of advanced small modular reactors - including modular high-temperature gas-cooled reactors and mobile microreactors - demands neutron transport codes capable of accurately resolving both thermal and fast neutron spectra, as well as complex geometries involving structured and unstructured meshes with rectangular or hexagonal boundary conditions. To rigorously validate such capabilities, we employ the three-dimensional TAKEDA benchmark, comprising four configurations: a light-water reactor with square lattice geometry, two fast breeder reactors (FBRs) in square arrangements, and a hexagonally configured FBR - encompassing a representative range of spectral and geometric challenges. Using SAAFCGSN, a second-order self-adjoint angular flux neutron transport code based on the finite element method, we perform full-core simulations of all four TAKEDA benchmark models. The computed effective neutron multiplication factors (keff) agree closely with reference solutions, exhibiting maximum relative deviations of 70pcm, 90pcm, 140pcm and 80pcm (1pcm = 10-5) across the configurations. Control rod worth predictions show maximum relative discrepancies of -4.42%, 2.50%, 1.02% and 1.60%, respectively. These results demonstrate high fidelity in both eigenvalue and reactivity coefficient predictions, validating the code's accuracy and robustness in modeling complex, three-dimensional reactor systems with mixed spectral and geometric features. Our findings establish SAAFCGSN as a reliable tool for high-fidelity neutronics analysis in next-generation small modular reactors.

The safe operation of small lead-based fast reactors (LFRs) requires ensuring that the core temperature remains within a safe range. High temperatures will intensify the corrosive effect of lead-bismuth (LBE) on structural materials, seriously affecting the core's lifespan. By burnable poisons (BPs) design, the risk of fuel and fuel rod cladding overheating under CRW accident in the LFR-180 core can be reduced. However, the core still faces the corrosion challenges induced by elevated LBE temperatures during and following the ULOF and ULOHS scenarios. In this research, the feasibility of the application of the self-actuated shutdown system (SASS) is explored, and the function of SASS is examined under anticipated transients without scram (ATWS). The calculation results demonstrate that the SASS can effectively mitigate the core equilibrium temperature following transients, thereby significantly reducing the risk of severe corrosion of structural materials. Designed in combination with SASS and BPs, the LFR-180BP-SASS improves the safety of the core during and following ULOF, ULOHS, and CRW events.

The space nuclear reactor power system (SNRPS), which uses a liquid metal-cooled reactor coupled with a closed-loop Brayton cycle for thermoelectric conversion, has emerged as the preferred choice for an advanced space power system. This preference is due to its excellent heat transfer efficiency in the core, wide power range, controllable equipment size, high power conversion efficiency, and mature technology. This study focuses on establishing a system transient analysis model for reactor design, control, and safety analysis of a SNRPS. The model includes subsystem models such as thermal-hydraulic models for the reactor core and primary coolant loop systems, power conversion unit models, and heat pipe radiator models. Six types of benchmark test problems are used to validate each sub-module and component model. The results show that the maximum absolute error between the sub-module model and the analytical solutions of these benchmark test problems is within 2%. Based on the theoretical model established, a transient analysis code for the space nuclear reactor (TACSNR) was developed. The TACSNR was verified using steady-state design parameters from the ultra-small liquid metal cooled space nuclear reactor power system concept (ULCR SNRPS) and the inherent safety sectored compact reactor with a SiGe thermoelectric (TE) power conversion assembly space nuclear reactor power system (SCoRe-TE SNRPS) startup transient process. The calculation results show that the maximum absolute deviation between the calculated values of the TACSNR and the steady-state design parameters of the ULCR SNRPS conceptual scheme is less than 1%, consistent with the parameter change trend and numerical values during the transient startup process of the SCoRe-TE SNRPS system. Additionally, the maximum relative deviation at rated steady state of the SCoRe-TE SNRPS is less than 12%.

In order to study the safety characteristics of the solid core space nuclear reactor power (SNRP) system under the maximum hypothetical accident, a two-dimensional entire core transient heat transfer analysis model was established, and the key parameters response characteristics of the ultra-small lithium-cooled SNRP under two maximum hypothetical accidents, namely, loss of heat sink (LOHS) and loss of coolant accident (LOCA), were calculated and analyzed. In the maximum hypothetical accidents, the coolant cooling capacity is lost, thus the core decay power is discharged into space only through the radiation of the residual heat removal system and the side surface of the reactor vessel. During the accidents, the heat transfer of the core deteriorated, and the fuel temperature may rise to the melting point, resulting in radioactive leakage. The results show that: (1) In the LOHS accident, the maximum fuel temperature reaches 2150 K at 550 s, and the pressure of the primary system volume accumulator continues to increase to the set system pressure safety limit of 2 MPa, resulting the primary loop overpressure failure. And the fuel matrix temperature is close to the set cladding limit temperature of 2200 K; (2) In the LOCA, the deterioration of heat transfer in the core makes the temperature increase rapidly, reaching a maximum of 3016 K at about 630 s, which is very close to the melting temperature of UN fuel 3123 K. As the decay power decreases, the maximum core temperature decreases to less than 1600 K after 24 h of the accident. The auxiliary cooling system of the solid core SNRP system under the maximum hypothetical accident is optimized, and the design parameters of the auxiliary cooling system meeting the safety requirements are obtained.

This paper elucidates a comprehensive derivation of the variational formulation pertaining to the static and spatial kinetics self-adjoint angular flux (SAAF) neutron transport equation. The methodology employed for discretization of the spatial variable is the finite element method, while the energy group discretization is executed via the group method, and the directional discretization is conducted using the discrete ordinates method. Analytic expressions for the discretization to variable separation under both vacuum and reflective boundary conditions are furnished. Constructed upon the MOOSE framework, a code designated as SAAFCGSN has been developed for the resolution of the SAAF neutron transport equation. The zero-order scattering matrix within this computational framework is managed through an innovative "decoupling" method, thereby enhancing the computational efficiency significantly. The functionality and robustness of the SAAFCGSN code are corroborated through meticulous evaluation involving seven distinct steady-state scenarios as well as two transient states. Empirical outcomes verify the compatibility of the SAAFCGSN code with both structured and unstructured mesh, inclusive of their amalgamations, thus facilitating maintenance and ensuring elevated computational accuracy. In addition, a performance analysis benchmarked against IAEA standards reveals that the adoption of the scattering matrix "decoupling" method propels a computational speed increase exceeding 30%, signifying a notable advancement in calculation efficiency.

BackgroundFast neutron pulsed reactors are sensitive to wall scattering neutrons, and their waveforms are changed by reflected neutrons. In addition, their operation may be adversely affected when there are too many reflected neutrons.PurposeThis study aims to solve the problem of fast neutron pulse reactor wall reflection neutron.MethodThe point reactor kinetic method containing the reflection effect, Monte Carlo method, and ANSYS were combined to analyze the Godiva-I transient process in fast neutron pulsed reactor with wall-reflected neutron effect. Firstly, the quench coefficient of the fast neutron pulsed reactor was calculated. Then, the point reactor kinetic method containing the reflection effect was established. Finally, the thermal power obtained from the neutronics calculation was combined with the ANSYS thermal-mechanical module to establish the thermal-mechanical calculation method for fast neutron pulsed reactor, and the effect of wall-reflected neutrons was analyzed and calculated.ResultsThe results show that the reflected neutrons increased the rear edge of the pulse. The reactivity decreases when the flat is washed whilst the core displacement and stress are improved.ConclusionsThe method established in this study can reasonably explain the phenomenon of reduction in attenuation and the increase in power after pulse.

Small lead-cooled fast reactors with a long lifetime generally refer to the core does not need refueling for a long time. The high excess reactivity and compact structure of the core restrict the design of control rod system. Therefore, effective reactivity control is the key to achieving longevity goals and safety enhancement. The study is carried out on a self-designed reactor LFR-180 with a reactivity swing of 6681 pcm. The combination of moderator and burnable poison (BP) is explored for reactivity compensation in the work. From the aspects of material selection, moderator design, and abundance optimization of BPs, a core control scheme is designed adopting ZrH1.6 as moderator and B4C as BP, which achieved a reasonable excess reactivity compensation. The abundance of 10B is determined according to the neutron fluence distribution in the core. The reactivity swing of the core could be reduced to 575 pcm. Although the moderator has certain unfavorable effects on power distribution and coolant void effect, the compensation design significantly improves the core safety margin under the CRW accident while the safety performance under ULOF and ULOHS transients needs further improvement. The simulation results in this paper provide ways for further design and research of small long-life LFRs.

Lead-based fast reactor (LFR) has been considered as one of the most promising concepts for Generation IV nuclear reactors. Subchannel analysis is frequently used to obtain the flow field and temperature distribution. Its applicability in lead-based wire-wrapped bundles has to be improved due to complex thermal-hydraulic characteristics. In this study, a refined subchannel analysis code, STAR-LFR, is developed. A refined fuel rod model is applied for circumferential non-uniform heat transfer, while a refined flow mixing module is applied for flow sweeping caused by wire spacers. Code validation with respect to crossflow distribution and heat transfer are conducted using high-fidelity large eddy simulation and experimental data, respectively. Besides, the code is applied in the thermal-hydraulic analysis of a non-uniformly heated fuel assembly. Overall, great ability on flow and heat transfer prediction are proved. The crossflow rate and the overheat caused by wire can be well estimated. This work provides a reliable tool that could support the thermal-hydraulic analysis as well as the design of LFR.

BackgroundMicro-reactors can be used as a lunar surface power or spacecraft power source for space exploration. Before launching the reactor, a safety analysis should be conducted to prevent a launch accident. Currently, the safety analysis of the radioactive isotope power system does not fully include the safety analysis of the reactor. The main critical safety analysis scenario is that the reactor falls and hits the concrete ground from a high altitude. The reactor may return to criticality after high-speed impact.PurposeThis study aims to investigate the nuclear safety characteristics of a space reactor subjected to dynamic shock under high-speed impact conditions.MethodsFirst of all, based on internal and surface unstructured grids, two simplified reactor models corresponding to two high-speed impact scenarios, i.e., pure fuel reactor vertical impact with ground, and cylinder reactor with a reflector layer and shielding layer impact the ground at a 30° angle were established. Then, the ABAQUS finite element method and unstructured mesh Monte Carlo method of particle transport were combined to predict the criticality properties of the pure fuel and cylindrical reactor during high-speed impact. Based on the surface and internal unstructured mesh Monte Carlo transport technology, the criticality safety analysis platform of micro-reactor under high speed impact was established.ResultsThe results show that the keff induced by the deformation may increase with time for the above mentioned two simplified reactors. The maximum increase in the keff of the pure fuel reactor can reach 1 000×10-5, whereas for the cylinder reactor, the keff is improved to a maximum of 200×10-5. Considering the non-uniform density effect, reactivities of -666×10-5 and -132×10-5 are introduced into the two reactors.ConclusionsThe critical safety characteristics of the reactor under different impact conditions should be evaluated to ensure sufficient safety margins under such accident conditions.

The inherent safety space reactor power system with a coupled thermoelectric conversion in a liquid metal lithium-cooled reactor represents a highly reliable space power. Compared with the ground reactor, the SNRPS has its own characteristics in safety considerations, mainly manifested in the SNRPS before launch, during launch and during the ascent into orbit will be affected by the launch vehicle. Which can be analyzed by the common methodology of probabilistic risk management. To investigate the response characteristics during in-orbit operation accidents, a transient analysis model of the liquid metal-cooled space reactor power system is established. The system response characteristics of the inherent safety space reactor power system conceptual designs are preliminarily analyzed under four potential typical in-orbit operating conditions, including (1) rated operating condition, (2) control drum misoperation events, (3) partial loss of coolant flow accident, and (4) partial failure of the radiator area accident. The results show that the power system has inherent safety in-orbit operation characteristics due to the system design operating parameters, which the coolant temperature below 1200 K at the rated operating condition. Even under typical operating accidents, the system coolant remains highly supercooled (more than 200 K), preventing boiling from occurring. The maximum temperature of the core fuel pin and cladding materials remains lower than their safety limits, ensuring that no core melting phenomenon occurs.

Due to the small size of the core, strong neutron leakage, and non-uniform distribution of core power and temperature in the Xi'an Pulsed Reactor (XAPR), there exists a complex coupling between the neutronicsthermalhydraulics behaviors within the reactor core. However, the influence of this coupling phenomenon on the transient behavior of the XAPR remains unclear, necessitating the performance of multi-physics coupling analysis. To this end, an integrated code named Nurus, which couples 3-D neutron diffusion spatial kinetics with thermal-mechanical solvers, has been developed and verified through benchmark problems, utilizing the opensource multi-physics coupling framework MOOSE. The multi-group cross-sections are calculated using the code NECP-X. The transient pulsed condition, featuring a reactivity of 3.45$, in the XAPR has been simulated by Nurus. The results demonstrate that the pulse peak power and FWHM (full width at half maximum) are in good agreement with the experimental data. The maximum radial expansion of the fuel element is approximately 1.3 x 10-4 m, resulting in a short-term contact between the fuel pellet and cladding. The developed code Nurus has been successfully employed in the safety analysis of transient experiments conducted on the XAPR.

The effect of excess Na2O on the properties of sodium beta-alumina solid electrolyte (BASE) was thoroughly investigated through relationships of the density, c-lattice parameter, beta ''-phase fraction, ionic conductivity and bending strength with the sintering temperature and the excess Na2O level. BASEs with a high level of excess Na2O showed a high density, a stable fraction of beta ''-phase, a high content of Na2O (small c-lattice parameter) and a fine grain microstructure when sintered at high temperature. BASE with a high level of excess Na2O also showed a high bending strength, but a high grain boundary impedance. The abnormal grain growth accounted for the seriously weakened bending strength and the greatly improved ionic conductivity in BASE with a low level of excess Na2O sintered at high temperature. Sintered at high temperature is a useful method for the sample with a high level of excess Na2O to obtain better conductivity and bending strength. These results are attributed to the varying roles of the excess Na2O in the sintering of BASE under different sintering temperature, including compensating the evaporation loss of Na2O, promoting the occurrence of transient ternary eutectic, and boosting the formation of secondary grain boundary phase. For better performance, the level of 6% excess Na2O is suggested as the optimized amount for a robust fabrication of BASE. Data availability: The raw/processed data required to reproduce these findings cannot be shared at this time due to technical or time limitations.

The lead-cooled fast reactor (LFR) is an important component of Generation-IV reactors, with many advantages and flexible applications. The evaluation and improvement of safety features have received special attention, especially when it comes to the application of new fuel types. The paper investigates the safety performance of LFRs with MOX, carbide, nitride, and metallic fuel in unprotected transient UTOP, ULOF and ULOHS. The core neutronics model is based on Monte-Carlo code OpenMC, by which the elementary reactivity feedback coefficients are calculated. The safety analysis model of the reactor primary circuit without scram transient is based on the one-dimensional point kinetic system code ASYST. The OpenMC-ASYST results are verified by the benchmark results of the ALFRED safety analysis. By learning from the state-of-the-art LFR designs with different advanced fuels, the core designs with MOX, carbide, nitride, and metallic fuel are separately proposed. The outcomes show that nitride and carbide fuel feature a higher potential safety margin over MOX fuel under unprotected transient scenarios. The safety potentials of metallic fuel vary in different transients. A sensitive analysis is applied to key parameters of different transients. The model and simulation results in this paper provide a reference for further design and research of lead-cooled fast reactors.

The Xi’an Pulsed Reactor (XAPR) is characterized by its small core size and integrated fuel moderator structure, which results in a non-uniform core power and temperature distribution. Consequently, a complex coupling relationship exists between its core neutronics and thermal hydraulics, necessitating the assurance for the operational safety of the XAPR. To optimize the experimental scheme in the reactor, a refined three-dimensional steady-state nuclear-thermal coupling analysis is imperative. This study focuses on investigating the coupling calculation of a three-dimensional steady-state neutronics and thermal-hydraulics model for the XAPR by utilizing an open-source multi-physical coupling framework known as Cardinal. The neutron transport equation is effectively solved using OpenMC, while a three-dimensional heat conduction model is employed to compute the heat conduction of the fuel elements. Furthermore, a parallel multi-channel model is utilized to determine the fluid heat transfer. The research is centered on the XAPR, whereby Monte Carlo and thermal-hydraulics coupling calculations of the core under steady-state full-power conditions are conducted, specifically at an operational capacity of 2 MW. The results demonstrate a strong agreement between the simulation and experimental outcomes. The maximum temperature recorded for the thermometric fuel element in the XAPR is 795.1 K, with a deviation of approximately −5.7% from the measured value. Moreover, the outlet fluid temperature of the thermal channel is observed to be 360 K, exhibiting a deviation of around −2.7% from the measured value.

Space nuclear reactor power,with the advantages of high energy density,high output power,long duration,and minimal influence from the external environment,is the preferred route for energy supply for future high-power long-life space missions and deep space exploration missions.Based on the developmental requirements and characteristics of different design options for megawatt-class space nuclear reactors,a technical scheme for a megawatt-class small lithium-cooled space reactor is designed.This scheme uses a lithium-cooled reactor coupled with a Brayton power conversion system that is lightweight and durable.The key technologies involved in the design are reviewed.Developmental progress of technical analysis and demonstration,verification prototype systems,and experimental platforms is presented.Suggestions and comments for developing high-power space nuclear power in China in the future are presented.

The fast-neutron burst reactor is a chain reactor that can operate in a prompt critical state. In order to ensure the operational safety of the fast-neutron-pulse reactor and prevent the supercritical pulse from causing physical damage to the material, it is necessary to simulate and analyze the pulse operating conditions of the fast-neutron-pulse reactor. Godiva-I is a spherical assembly of highly enriched uranium metal made during the 1950s. A prompt-critical transient in such a nuclear system impels a quick power excursion, which will cause a temperature rise and a subsequent reactivity reduction because of the metal sphere’s expansion. The overall transient lasts for a few fractions of a millisecond. Based on the point kinetics and Monte Carlo method, the temporal and spatial characteristics of transient input power were calculated, the difference of the average reactivity temperature coefficient between uniform density and non-uniform density was compared, and the transient power distribution condition was loaded into the thermal–mechanics calculation of the MOOSE platform; thus, the pulse process of Godiva-I with different initial reactivity periods was simulated. The JFNK (Jacobian–Free–Newton–Krylov) direct method and multi-app indirect method were used to analyze the transient response of the pulse dynamic process using the heat conduction module and tenor mechanics module, respectively. After considering the influence of the inertia effect and wall-reflected neutrons, the simulation results were much closer to the experimental values. Based on the stochastic tools module, the uncertainty propagation and sensitivity analysis of the Godiva-I model were carried out, the uncertainty of external surface displacement of Godiva under input disturbance of material properties and heat source amplitude factor was obtained, and the sensitivity of different input parameters to output parameters was quantified. The research results can lay a technical foundation for the thermal–mechanics coupling analysis and uncertainty quantification of the metal fast reactor.

Lead-based cooled fast reactor (LFR) has been considered as one of the most promising concepts for GEN IV nuclear systems. Due to its intrinsic safety and good neutron economy, LFR has a great prospect in reactor miniaturization and modularization. Different from PWR, peak cladding temperature should be the most important safety limit in the thermal-hydraulic design of LFR. And sub-channel analysis is a frequently used method to obtain the distribution of coolant and cladding temperature. In this study, a refined sub-channel analysis code available for lead-bismuth eutectic （LBE） coolant, STAR-PB, is developed. Fundamentally, physical properties, heat transfer correlations, pressure drop models and turbulent mixing models were investigated and implemented into the code. In view of high thermal conductivity of lead-based coolant, its lateral thermal conduction effect was also taken into account. Moreover, considering that wire spacer is notably used in fuel assembly designs for LFR, a distributed resistance model was applied to reveal its enhanced mixing effect on flow field. Code validation was performed by two steps. Firstly, our simulation results about a 7–pin wire-wrapped bundle were compared with that from high-fidelity large eddy simulation performed at Argonne National Laboratory. Ability of our code in local flow field prediction was well verified. Secondly, experimental data of 19-pin bundle with wire spacer presented by Karlsruhe Institute of Technology in 2016 were selected for the validation of STAR-PB. Its high reliability on heat transfer prediction of LBE-cooled wire-wrapped bundle was well proved. In the future, STAR-PB will support the study on the key issue about thermal-hydraulic analysis as well as the design of LFR.

Sodium bromide is used as an additive to modify the sintering and conductive properties of sodium beta alumina solid electrolyte (BASE) through the halogen effect. The present study investigates the effect of NaBr on the sintering behavior, phase composition, ionic conductivity and mechanical strength of BASE. BASE with a high content of NaBr showed a high open porosity, and retarded densification at higher temperature. BASE with a high proportion of NaBr also exhibited a low relative beta"-phase content and a large c-lattice parameter. BASE with 1% ratio of Br anions was found to possess the largest proportion of abnormal grains in the microstructure among other BASEs, with the ratio of Br anions ranging from 0 to 2%. BASE with 1% ratio of Br anions also exhibited the highest conductivity and a better bending strength. These results are attributed to the volatilization of NaBr and the possible reaction between the Br anion and the Al-O bond at the particle surface. NaBr could effectively tailor the grain size and ionic transport at the grain boundary in BASE. Due to the less amount of grain-boundary phase and a suitable proportion of abnormal grains, BASE with 1% ratio of Br anions showed an excellent ionic con-ductivity of 1.01 mS cm-1 at 20 degrees C and a moderate bending strength of 186 MPa. This study suggests that the ionic conductivity in BASE can be increased by incorporating Br anions, and thus, offers some insights into the effect of anions on the properties of BASE.

A continuous finite element method (FEM) based on B-spline wavelet on the interval (BSWI) is proposed to solve the first-order neutron transport equation with discrete ordinate (SN) angular discretization. Two technologies are applied in this method, one of technologies is that the streamline upwind Petrov-Galerkin (SUPG) method is utilized to stabilize the first-order neutron transport equation when the FEM is used. Another is that the scaling functions of BSWI are applied to replace the usual Lagrange basis function. Based on the above two technologies, the stabilized weak form of neutron transport equation applying the SUPG technology based on BSWI is derived. Finally, some numerical examples are utilized to verify the proposed method. The results demonstrate that the method can treat the void region prob-lem, and compared the FEM with SUPG technology, it can obtain fast convergence and numerical preci-sion under the condition of much less grid. Overall, this method has good accuracy, high computational efficiency and wide application. (c) 2022 Published by Elsevier Ltd.