Reactor Safety Analysis Research Articles

SAM: A Modern System Code for Advanced Non-LWR Safety Analysis

The System Analysis Module (SAM), developed at Argonne National Laboratory and by collaborators at other organizations, is for advanced non–light water reactor safety analysis. SAM aims to provide fast-running, modest-fidelity, whole-plant transient analysis capabilities that are essential for fast-turnaround design scoping and engineering analyses of advanced reactor concepts. To facilitate code development, SAM utilizes the MOOSE object-oriented application framework, its underlying finite element library, and linear and nonlinear solvers to leverage modern advanced software environments and numerical methods. SAM aims to solve tightly coupled physical phenomena, including fission reaction, heat transfer, fluid dynamics, and thermal-mechanical responses in advanced reactor structures, systems, and components with high accuracy and efficiency. This paper gives an overview of the SAM code development, including goals and functional requirements, physical models, current capabilities, verification and validation, software quality assurance, and examples of simulations for advanced nuclear reactor applications.

Estimation of Turbulent Mixing Factor and Study of Turbulent Flow Structures in Pressurized Water Reactor Sub Channel by Direct Numerical Simulation

Abstract Subchannel analysis codes are presently a requirement for design and safety analysis of nuclear reactors. Among the crucial inputs for these codes, the turbulent mixing factor holds particular significance. However, acquiring this factor through experimental means proves to be a challenging endeavor, primarily due to the necessity for precise pressure equilibrium between subchannels. Consequently, this requirement leads to the undertaking of expensive and intricate experiments for each new reactor or in cases where there are modifications in fuel bundle design. The need for direct numerical simulation (DNS) stems from the challenges and costs involved in experimental techniques, and the uncertainties due to empiricism in computational fluid dynamics (CFD) models. In this study, DNS has been conducted across six Reynolds numbers, ranging from 17,640 to 1.176 × 105, in the geometry of a pressurized water reactor (PWR) subchannel. The resulting turbulent flow structures have been computed and their dynamics are examined. Furthermore, this paper presents a methodology for directly calculating the turbulent mixing factor from the fluctuating velocity field obtained from DNS data. The turbulent mixing process has been scrutinized in-depth, and a correlation for the turbulent mixing factor is developed. It is noted that most of the mixing occurs in the near-wall region. The study suggests different mixing factors for mass and momentum mixing. This paper aims to provide a comprehensive insight into the turbulent mixing phenomenon.

Numerical investigation on the core thermal hydraulic behavior of pool-type sodium-cooled fast reactor (SFR)

A thorough understanding of the reactor core thermal hydraulic behavior is essential for the design and safety analysis of Sodium-cooled Fast Reactors (SFR). Due to the application of hexagonal subassembly, the core thermal hydraulic behavior is significantly affected by the flow field within the subassemblies, the inter-wrapper region and the hot pool. Analysis of the core thermal hydraulic behavior requires a model coupling the three regions mentioned above, which has been identified as one of the thermal hydraulic challenges in SFR. In the present study, a 3D model that covers the three regions was developed for the core of the China Experimental Fast Reactor (CEFR) with the Computational Fluid Dynamic (CFD) code, Fluent. The inter-wrapper region and the hot pool were modeled in detail, while the subassemblies were modeled with a special porous medium model. The core thermal hydraulics behavior under steady state was studied, more specifically, information for the flow field distribution at the core outlet, the inter-wrapper flow and the duct wall temperature distribution was obtained. Under steady state, liquid sodium in the inter-wrapper region is supplied by the inner region of the hot pool. And it enters the inter-wrapper region from the core outer region and returns back to the hot pool inner region from the core central region. The inter-wrapper flow is cooled by non-fuel subassemblies and heated up by fuel subassemblies. For non-fuel subassembly, the ratio of the total heat transfer rate between the inter-wrapper flow and the subassemblies to the heat generated within subassemblies could reaches 96%; for fuel subassemblies, the maximum ratio of the total heat transfer rate between the inter-wrapper flow and the subassemblies to the heat generated within subassemblies is 2.45%. Significant temperature gradients have been observed on the duct wall, with maximum values of 156.69 K/m in the vertical direction and 2,196.00 K/m in the circumferential direction. The largest temperature gradient appears on the duct of subassemblies adjacent to the transition region of fuel subassemblies and non-fuel subassemblies.

Parametric Analysis of the Compact and Long-Term-Operable Passive Residual Heat Removal System

Differing from land-based systems, conventional passive residual heat removal systems (PRHRSs) in nuclear-powered ships encounter challenges for use as safety systems due to limited space and difficulties in adopting safety aids. To resolve this problem, the authors have previously suggested a compact and long-term-operable PRHRS that uses air cooling and seawater cooling in tandem, and its feasibility was confirmed through a design study and transient analysis. Nevertheless, the system performance depends on various parameters, and their sensitivities have yet to be analyzed. The purpose of the current study is to conduct a parametric analysis of the system focusing on four parameters: filling ratio, thermal center difference between heat source and sink, heeling angle, and heat source temperature. The Multi-dimensional Analysis of Reactor Safety (MARS-KS) code was used for the parametric analysis. The results show that the parameters are highly interrelated with each other, and consequently, the system exhibits significantly different behavior depending on the parameter conditions. In particular, the filling ratio determines the overall trends of the system. It was also found that the presence of two heat sinks with a single heat source in the natural circulation loop of the system complicate the natural circulation behavior. Based on the results, we conclude that a thorough examination and careful control of the parameters are necessary to implement the proposed system. The highlights are as follows: 1. Parametric analysis of compact and long-term-operable PRHRS is conducted. 2. Analysis reveals that the filling ratio is the most dominant parameter for system performance. 3. The unique behavior of the natural circulation loop with two heat sinks and a single heat source is analyzed.

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.

Verification and Demonstration of One-Dimensional Freezing Model in SAM for Salt-Cooled Reactor Analysis Applications

This work presents the development and implementation of the one-dimensional freezing model in system analysis code SAM (System Analysis Module), code verification using analytical solutions, and code demonstration of a postulated overcooling transient for a fluoride salt–cooled high-temperature reactor (FHR) system and safety analysis applications. This paper first summarizes the freezing model, finite element numerical method, and special numerical treatment for handling transitions between single- and two-phase conditions. Analytical solutions are derived for two cases, with and without solid walls, for code verification purposes. As expected, the numerical results predicted by SAM agree very well with the analytical solution. A code demonstration is then performed on a postulated protected overcooling transient event of a generic reference pebble bed FHR design. The code was found to successfully predict salt freezing during such a postulated event. However, due to the lack of salt freezing testing data, code validation is not performed in this work, but will be pursued in future studies when such data become available.

Validation and parametric study of FFRD model in DRACCAR code

The recent revision of Emergency Core Cooling System (ECCS) regulations in Korea has necessitated the consideration of Fuel Fragmentation, Relocation, and Dispersal (FFRD) phenomena in nuclear reactor safety analyses. Consequently, the Korea Atomic Energy Research Institute (KAERI) has developed and integrated the FFRD model into the domestically licensed safety analysis code, SPACE. Globally, US NRC’s FRAPTRAN and IRSN’s DRACCAR are available for evaluating FFRD phenomena. The FRAPTRAN code incorporates the FFR model, developed by Quantum Technology, while the fuel dispersal model is currently not included. In contrast, the DRACCAR code functions as an integrated analysis platform capable of modeling multi-dimensional thermal, hydraulic, mechanical, and chemical phenomena during a Loss of Coolant Accident (LOCA). This study conducts a thorough examination of the FFRD model in the DRACCAR code and validates its applicability through analysis using the Halden IFA-650 tests. The results demonstrate satisfactory predictive capabilities. Furthermore, a parametric study of key FFRD model parameters enhances the understanding of the FFRD model in the DRACCAR code. The development of detailed physical models in the FFRD model could significantly enhance the performance of the DRACCAR code, warranting the establishment of a comprehensive framework for these advancements. In the future, code-to-code comparisons between the DRACCAR code and other domestically developed integrated analysis platforms will be conducted to investigate various phenomena in depth.

Coupling of the best-estimate system code and containment analysis code and its application to TMLB’ accident

With the development of advanced pressurized water reactor technology, the thermal-hydraulic coupling effect between the containment and the primary system becomes increasingly tight. In order to meet the demand for integrated safety analysis between the containment and the primary system, this paper investigates a direct coupling method between the best-estimate system code Advanced Reactor Safety Analysis Code and the containment analysis program ATHROC (Analysis of Thermal Hydraulic Response Of Containment). The feasibility of this direct coupling method and the applicability of the coupled program for overall safety analysis are demonstrated using Marviken two-phase flow release experiments. The ATHROC/ARSAC coupled program is employed to analyze the impact of the pressure relief function of the CPR1000 nuclear power plant pressurizer on the behavior of the primary system and containment during the TMLB’ accident. The calculation results indicate that these measures can reduce the pressure of the primary system to the level acceptable by the low-pressure injection system, but at the same time, they cause the pressure in the containment to rise to nearly 0.4 MPa. Therefore, to ensure the structural integrity of the containment, it is necessary for the non-passive hydrogen recombiner to effectively reduce the hydrogen concentration, thereby avoiding additional pressure increase in the containment due to hydrogen deflagration, which could lead to overpressure failure. The findings of this study are of significant reference value for improving the safety performance of thermal-hydraulic systems in operational Gen-II and advanced Gen-III pressurized water reactor nuclear power plants.

Verification of the SAM Code by Means of the Method of Manufactured Solutions: Application to Molten Salt Reactor Multiphysics Simulation

Software verification and validation constitute crucial phases in the development of simulation computer codes, particularly in the context of nuclear reactor safety analysis codes, where stringent safety requirements govern the development and deployment of nuclear technologies. This paper focuses on numerical verification study of the System Analysis Module (SAM) computer code, currently under development at Argonne National Laboratory. Specifically, we employed the Method of Manufactured Solutions (MMS) and proposed a verification technique tailored to the multiphysics simulation of molten salt reactors (MSRs). This research accomplished three main objectives. First, we have addressed key challenges associated with applying the MMS to MSR systems, arising from (1) the complex multiphysics coupling inherent in this problem and (2) the necessity to model the entire coolant loop for describing the drift of delayed neutron precursors outside the reactor core. The paper provides recommendations and guidelines to overcome these challenges, enabling the successful application of the MMS for simulating MSRs. Second, we have presented a comprehensive set of verification examples, serving as an exhaustive benchmark for code verification within the nuclear community. Third, we have established a robust verification of the SAM code’s capability to model MSR systems.

Application of BPNN algorithm in thermal-hydraulic analysis of unwrapped LFR core

Due to the complex structure of the LFR fuel rod bundle, refined CFD simulation consumes significant computing resources and time, making it difficult to meet the immediate needs of engineering design and research. This paper introduces a method that integrates the sub-channel level thermal-hydraulic analysis code CorTAF-LBE with the BPNN algorithm to analyze the thermal-hydraulic phenomena within the LFR core. The method has been validated by refined simulation results of the THEADES test section, which indicate that the error is within an acceptable range. The feasibility of its application in LFR fuel assemblies was also evaluated. The flow characteristics and temperature distribution in unwrapped LFR rod bundles are investigated. Due to differences in fuel distribution and flow area, the temperature in the central channel is much higher than that in the side and trapezoidal channels. Three accident conditions, including inlet blockage, center blockage, and outlet blockage, were simulated. The corresponding peak temperatures of the fuel cladding were 670 K, 767 K, and 860 K, respectively, representing an increase of approximately 170 K compared to the nominal conditions. The analysis results effectively demonstrate the 3D temperature distribution of the fluid in the rod bundles, which is significant for reactor design and safety analysis of LFRs.

Enhancement of Reflood Test Prediction by Integrating Machine Learning and Data Assimilation Technique

Data assimilation (DA) was revealed as a highly efficient approach to enhance the prediction’s accuracy, demonstrating the reliability of the simulation through uncertainty quantification analysis. However, in the numerical simulations, most of the tasks are highly nonlinear relationships between the parameters that directly affect the efficiency of the DA such as the large search space dimension, resulting in significant computational costs. This limitation can be overcome by implementing machine learning (ML) predictions that can efficiently expand the DA search space. Therefore, this study is aimed at enhancing the performance of DA by integrating ML and DA (IMD), proposing a new method to overcome the stand-alone DA limitations. The approach involved implementing a stand-alone DA using the multidimensional analysis of reactor safety (MARS) code to enhance the prediction of reflood tests. The output datasets obtained from the stand-alone DA were then used to train the deep neural networks (DNNs), and the accuracy of the DNN’s prediction was thoroughly evaluated with varying dataset sizes. This DNN subsequently can predict the enormous unobserved samples, enabling the identification and investigation of the prospective candidates for the subsequent DA process. The results demonstrated that the stand-alone DA achieved an accuracy enhancement of up to 41.3% in reflood test predictions, while the IMD yielded even more significant improvements, with a performance enhancement of 47.0%. These findings reveal that the IMD approach outperformed the stand-alone DA approach, particularly in the case of high flooding rate tests. In this context, the proposed integrating system can effectively overcome the high computational cost and enhance the performance of stand-alone DA.

Experimental investigation of quench front propagation during reflooding in 5 × 5 rod bundle channel with axial uniform power distribution

This experimental study delves into the impact of inlet injection velocity, inlet subcooling, and linear power density on the quench front propagation during reflooding in 5x5 rod bundle channel with axial uniform power distribution. The investigation utilized a film boiling test facility constructed by NUclear Safety and Operation Laboratory (NUSOL) of Xi'an Jiaotong University. The findings demonstrate a discernible sensitivity of the quench front to variations in these parameters, wherein higher linear power density, reduced flow rate, and decreased coolant subcooling lead to delayed reflooding. Moreover, the study derived the surface parameters of the heater rod use self-developed Reflooding Experimental Data Analysis code (REDA). The comprehensive experimental data and empirical models generated in this study hold significant potential for enhancing the safety analysis of nuclear reactors.

A new surrogate method for the neutron kinetics calculation of nuclear reactor core transients

Reactor core transient calculation is very important for the reactor safety analysis, in which the kernel is neutron kinetics calculation by simulating the variation of neutron density or thermal power over time. Compared with the point kinetics method, the time-space neutron kinetics calculation can provide accurate variation of neutron density in both space and time domain. But it consumes a lot of resources. It is necessary to develop a surrogate model that can quickly obtain the temporal and spatial variation information of neutron density or power with acceptable calculation accuracy. This paper uses the time-varying characteristics of power to construct a time function, parameterizes the time-varying characteristics which contains the information about the spatial change of power. Thereby, the amount of targets to predict in the space domain is compressed. A surrogate method using the machine learning is proposed in this paper. In the construction of a neural network, the input is processed by a convolutional layer, followed by a fully connected layer or a deconvolution layer. For the problem of time sequence disturbance, a structure combining convolutional neural network and recurrent neural network is used. It is verified in the tests of a series of 1D, 2D and 3D reactor models. The predicted values obtained using the constructed neural network models in these tests are in good agreement with the reference values, showing the powerful potential of the surrogate models.

CFD modelling of flashing flows for nuclear safety analysis: possibilities and challenges

Abstract Because of its relevance for the safety analysis of pressurized water reactors (PWR), many research activities on flashing flows in pipes and nozzles arose from the mid of last century. Most of them have been focused on the critical mass flow rate and transient pressure or temperature fluctuations by means of experiments and system codes. Since the beginning of this century, owing to the increase in computer speed and capacity, computational fluid dynamics (CFD) is being used more and more in the investigation of flashing flows, which has the advantage of providing three-dimensional insights in the internal flow structure as well as its evolution. This work presents an overview of relevant flashing scenarios in the nuclear safety analysis, and focuses on the discussion about possibilities and challenges of using CFD modelling. It is shown that a two-fluid model with the thermal phase-change model is superior to a mixture model with pressure phase-change, relaxation and equilibrium models, respectively, in terms of interfacial mass transfer, however, efforts are still required to improve the interphase heat-transfer model. Furthermore, since flashing is accompanied with high void fraction and broad bubble size ranges, a poly-disperse two-fluid model is recommended, but the effect of phase change on bubble coalescence and breakup needs further research. In addition, during flashing the flow pattern may change from single phase to bubbly flow, churn flow, annular flow, and even mist flow. The rapid change of interfacial topology as well as its influence on the applicability of closure models remains a challenge.

Development and application in multiscale and multiphysics methodologies in Spain: Present and future trends

In the field of reactor physics analysis, the coupling of multiple physics phenomena plays a crucial role in enhancing the accuracy of predictions and understanding complex systems. Multiphysics refers to the study and analysis of physical phenomena that involve multiple interconnected physical processes occurring simultaneously in a nuclear system to ensure essential aspects of reactor design, safety analysis, and optimization, among others. Multiphysics encompasses various domains of physics, such as Thermal-Hydraulics, Neutronics, Structural Mechanics, Radiation Transport, Chemistry, and Materials Science. On the other hand, the Multiscale approach involves combining high-fidelity models with lower-fidelity ones to accurately capture the relevant physical phenomena in a Nuclear Power Plant (NPP). Multiscale involves three main scales: system level, core level, and detailed analysis scale. This paper presents an overview of the main research performed by Spanish groups in the field of multiphysics and multiscale calculations, particularly on thermal–hydraulic analysis. This revision is focused mainly on two key aspects: thermal–hydraulic multiscale coupling and thermal–hydraulic / neutronic coupling. The paper also includes the expected future trends in this field.

The transformative role of Computational Fluid Dynamics (CFD) in chemical engineering

Chemical engineering is a discipline intrinsically linked to fluid behavior. From reaction kinetics to reactor design, understanding how fluids flow, mix, and transfer heat is paramount. Traditionally, this relied heavily on experimentation, a time-consuming and resource-intensive process. The emergence of Computational Fluid Dynamics (CFD) has revolutionized the field, offering a powerful in-silico approach to analyze fluid dynamics in chemical engineering processes. This review paper explores the transformative role of CFD, examining its impact on various aspects of chemical engineering, including reactor design, optimization, process intensification, scale-up, and safety analysis. The paper also discusses the challenges associated with CFD simulations, ongoing advancements in the field, and potential future directions.

Analytic Error Analysis of the Partial Derivatives Cross-Section Model—I: Derivation

Accurate assessment of uncertainties in cross-section data is crucial for reliable nuclear reactor simulations and safety analyses. In this study, we focus on the interpolation procedure of the partial derivatives (PD) cross-section model used to evaluate nodal parameters from pregenerated multigroup libraries. Our primary objective is to develop a systematic methodology that enables prediction of the incurred errors in the cross-section model, leading to the development of optimal case matrices, more efficient cross-section models, and informed case matrix construction for reactor types lacking substantial data and experience. We make progress toward this objective through a rigorous analytic error analysis enabled by the derivation of error expressions and bounds for the PD model based on the discovery that the method is a form of Lagrange interpolation. Our investigations reveal distinct outcomes depending on the chosen cross-section functionalizations, achieved by identifying the sources of error. These error sources are found to include interpolation error, which is always present, and model form error, which is a property of the supplied case matrix. We show that simply increasing grid refinement through the addition of branches may not always lead to decreased cross-section errors, particularly in cases where the model form error predominantly contributes to the total error. We present numerical results and verification in a companion paper, showing these different error characteristics for various cross-section functionalizations. Although applied to current light water reactor environments, our methodology offers a means for advanced reactor analysts to develop case matrices with quantified error levels, advancing the goal of a general methodology for robust two-step reactor analysis. Future work includes exploring different lattice types and functionalizations, extending reactivity bounds to multilattice problems, and investigating historical effects within the macroscopic depletion model.

Time Dependent Energy Deposition Model in RMC Kinetics Calculation

Calculating or predicting the energy deposition in the reactor is an important task for reactor design and safety analysis. Rigorous energy deposition estimation is a difficult task because of the energy dependence, spatial dependence, and time dependence of in-core nuclear heating. This paper develops a time-dependent energy deposition model in the RMC kinetics calculation to explicitly account for the time-delay effect of delayed in-core nuclear heating. An explicit sampling method (ESM) is proposed to sample the decay time of the delayed photon and beta precursors based on a new precursor library processed from the ENDF/B-VIII.0 library. The new model is verified by comparing it with the typical equilibrium model using the Godiva experiment and the C5G7- TD benchmark. Maximum 2.5% and 5.4% relative deviations are observed in GODIVA and C5G7-TD cases respectively, which indicates that the equilibrium model underestimates the energy deposition over the transient time. The analysis of the energy deposition results demonstrates that the new model can provide more precise energy deposition estimation in the transient calculation.

Experimental measurement of stiffness coefficient of high-temperature graphite pebble fuel elements in helium at high temperatures

Graphite material plays an important role in nuclear reactors especially the high-temperature gas-cooled reactors (HTGRs) by its outstanding comprehensive nuclear properties. The structural integrity of graphite pebble fuel elements is the first barrier to core safety under any circumstances. The correct knowledge of the stiffness coefficient of the graphite pebble fuel element inside the reactor's core is significant to ensure the valid design and inherent safety. In this research, a vertical extrusion device was set up to measure the stiffness coefficient of the graphite pebble fuel element by the Institute of Nuclear and New Energy Technology (INET) of Tsinghua University in China. The stiffness coefficient equations of graphite pebble fuel elements at different temperatures are given (in a helium atmosphere). The result first provides the data on the high-temperature stiffness coefficient of pebbles in helium gas. The result will be helpful for the engineering safety analysis of pebble-bed nuclear reactors.

Safety analysis of pressurized water reactors with annular fuel during different transients

The dual-cooled annular fuel has two channels, with a shorter heat transfer path and a larger heat transfer area than solid fuel, which can effectively improve the safety of the reactor. It has excellent potential to improve the economy of the pressurized water reactor (PWR) and is considered to have a good development prospect. In this paper, the safety of the reactor with annular fuel assemblies under different transient conditions is analyzed using the system code NUSOL-SYS and the subchannel code NACAF, with the CPR1000 as the reference power plant. The analysis mainly includes the large break loss of coolant accident (LBLOCA), main steam line break accident (MSLB), loss of flow accident (LOFA), and rod ejection accident (REA) under nominal power and higher power density. The flow blockage accident and the combined accidents of LBLOCA and the flow blockage accident are also evaluated. The results show that during LBLOCA, the peak cladding temperature (PCT) of the core is only 833 K, much lower than that of the solid fuel. In addition, the departure from nucleate boiling ratio (DNBR) of annular fuel is larger during MSLB and LOFA, which means a more negligible risk of fuel damage. In REA, the average temperature of annular fuel is below 900 K, and the average enthalpy is below 200 kJ/kg, which is much lower than that of solid fuel. The results at 150 % power show that the performance of the core with annular fuel is still better than that of solid fuel at nominal power, except that the PCT during LBLOCA is slightly higher than solid fuel at nominal power. During the flow blockage accident, the results with different blockage areas show that a small proportion of blockage of the inner channel does not have a significant effect on the cladding temperature and that there is a risk of rupture when the inner channel is completely blocked. Finally, the results of the assumed combined accident show that the blockage of the inner channel before scram will significantly increase the PCT of the core and the time to complete the reflood during LBLOCA.