Reactor Physics Research Articles

Reactivity calculation in molten salt reactors with inverse kinetics model

Most molten salt reactor designs present a liquid fuel that, mixed with the coolant composed of molten salts, circulates through the reactor. This circulation introduces important phenomena in the study of reactor physics, thus requiring changes in the existing physical models applied in conventional reactors with solid fuel. One of the main influences of the fuel flow in the reactor is in the delayed neutron precursors’ concentration, which partially decay outside the core, not contributing to the fission chain reaction. In this paper, we investigate the physical models used for this type of reactor, especially the neutron point kinetics, in order to develop an inverse kinetics model, which has practical applications such as core reactivity monitoring. We develop a semi-analytical solution for the proposed model, which is used to solve two transients: a linear variation between power levels, and the determination of criticality regions during a decrease in flow velocity.

Reactor physics characterization of triply periodic minimal surface-based nuclear fuel lattices

Triply periodic minimal surface (TPMS) lattices are receiving substantial attention in numerous engineering fields due to their impressive topology-driven physical characteristics. TPMS lattices are periodic structures of two distinct intertwined volume domains separated by an area-minimizing surface or wall. TPMS lattices have been observed in nature, such as biological membranes, skeletons, block copolymers, sea urchins, butterfly wings, and equipotential surfaces in crystals. Intriguingly, the topology of TPMS lattices can be easily parametrized via level-set equations and thus are heavily numerically and experimentally studied. A significant research effort is currently applying TPMS lattices for heat exchangers and sinks. This paper extends TPMS lattice applications to nuclear reactor fuel designs, with a focus on identifying relevant TPMS geometric parameters controlling neutronics characteristics, such as reactivity, neutron spectrum, and heat removal properties. We found that fuel surface-area-to-volume ratios for TPMS lattices can be two orders of magnitude larger than current cylindrical fuel rods. Further, the selected TPMS lattice and its implicit equation, the unit cell pitch, wall thickness, and structure porosity are design parameters enabling neutronics optimization for both thermal and fast spectrum configurations, paving the way for exceptionally compact and dense nuclear core concepts.

Uncertainty reduction of sodium void reactivity using data from a sodium shielding experiment

ABSTRACT This study investigated the feasibility of reducing the uncertainty associated with fast-reactor-core design by sharing an experimental database between different fields (e.g. reactor physics and radiation shielding) using data assimilation techniques. As the first step in this study, we focused on the ORNL sodium shielding experiment and investigated the possibility of using the experimental data to reduce the uncertainty in sodium void reactivity (SVR), which is the most important safety parameter for sodium-cooled fast reactors. A sensitivity analysis based on the Generalized Perturbation Theory was performed for the sodium shielding experiment. Using the sensitivity coefficients evaluated here and those of the sodium void reactivity previously evaluated by the JAEA, we showed that sodium shielding experimental data can contribute to the uncertainty reduction of SVR by adopting the cross-section adjustment method. Based on this study, the uncertainty reduction effect is expected to be significant, especially for SVR dominated by neutron-leakage phenomena. Although new reactor physics experimental data on SVR may be difficult to obtain, the results of this study suggest that data from sodium shielding experiments can partially substitute for this role. This study demonstrated the value of the mutual use of integral experimental data in fast reactor designs.

Evaluation of SCALE, Serpent, and MCNP for Molten Salt Reactor applications using the MSRE Benchmark

The International Reactor Physics Benchmark Experiment’s MSRE benchmark provides zero-power critical validation data that has been used to assess the accuracy and consistency of SCALE, MCNP, and Serpent for design and licensing of a modern MSR. The codes were used to model the benchmark and a wide range of variations in the geometry, nuclear data library, code versions, and problem specifications. Most of these cases demonstrated excellent consistency, within two standard deviations of the stochastic error, for the reactivity and associated reactivity worth of the variation. However, the codes over-predicted the initial criticality of the MSRE by 3%, which is larger than the provided experimental uncertainty. It was shown that care must be taken to ensure that the bound scattering treatment is consistent with comparing codes. It was also shown that for the MSRE, the use of the ENDF/B-VII.0 library introduced a significant increase in the reactivity (>200 pcm). Code predictions for two coefficients of reactivity (fuel and isothermal) were validated with data from the MSRE and were well within the experimental uncertainty, thus providing confidence in each code to provide accurate data for safety analysis calculations. These results provide quantifiable estimates of the computational variation one could expect due to the choice of any one of these codes, or a particular nuclear data library, for both initial criticality and reactivity coefficients.

Optimal rule based fuzzy-PI controller for core power control of nuclear reactor

In this paper, an optimal rule based fuzzy proportional integral controller is proposed to control the core power of the molten salt breeder reactor (MSBR) model. Firstly, a nonlinear MSBR model is considered. It is then linearized using the perturbation linearizing approach, and the transfer function of the linearized MSBR system is established. Secondly, an optimal Fuzzy-PI control structure is formulated where a PI controller is set as the principal controller for the MSBR model and a fuzzy control system is used to adjust the PI controller parameters during any disturbance in the MSBR. The rule base system of the fuzzy controller is optimized with a reshaped class topper optimization algorithm. Finally, the optimized Fuzzy-PI controller tests under a variety of conditions. Furthermore, the Nyquist stability approach is used to analyze the stability of the closed loop MSBR model.

Influence of biochar derived from sugarcane bagasse at different carbonization temperatures on anammox granular formation

Biochar derived from sugarcane bagasse, carbonized at temperatures of 300, 550, and 800 °C, exhibit different characteristics, such as pH, functional groups, specific surface area, and released nutrients. These three types of biochar were separately added into the enriched anammox cultures, influencing granular formation and nitrogen removal. The addition of biochar300 proved to be the most effective in stimulating anammox granular formation. On day 141 of operation, granular size >1.40 mm could be observed in all 3 biochar-amended reactors. The volatile suspended solids of these granules increased 3.2-fold, 1.2-fold, and 1.8-fold respectively compared to the reactor control without biochar addition. Furthermore, both short-term and long-term investigations of biochar addition demonstrated that biochar300 consistently promoted anammox activity surpassing additions of biochar550 and biochar800, especially during the start-up period. Based on various biochar300 dosing experiment, the higher doses may indicate higher electron exchange capacity. However, doses at levels ≥20 g L−1 negatively impacted the performance of the anammox system. The addition of biochar550 and 800 led to crystal accumulation and precipitation within granules. The crystals were identified as calcite, carbonate hydroxyapatite, and hydroxyapatite by using the XRD technique. Moreover, microbial community after the long-term biochar addition was analyzed by using next-generation sequencing technique.

Computation of High-Order Sensitivities of Model Responses to Model Parameters—I: Underlying Motivation and Current Methods

The mathematical/computational model of a physical system comprises parameters and independent and dependent variables. Since the physical system is seldom known precisely and since the model’s parameters stem from experimental procedures that are also subject to uncertainties, the results predicted by a computational model are imperfect. Quantifying the reliability and accuracy of results produced by a model (called “model responses”) requires the availability of sensitivities (i.e., functional partial derivatives) of model responses with respect to model parameters. This work reviews the basic motivations for computing high-order sensitivities and illustrates their importance by means of an OECD/NEA reactor physics benchmark, which is representative of a “large-scale system” involving many (21,976) uncertain parameters. The computation of higher-order sensitivities by conventional methods (finite differences and/or statistical procedures) is subject to the “curse of dimensionality”. Furthermore, as will be illustrated in this work, the accuracy of high-order sensitivities computed using such conventional methods cannot be a priori guaranteed. High-order sensitivities can be computed accurately and efficiently solely by applying the high-order adjoint sensitivity analysis methodology. The principles underlying this adjoint methodology are also reviewed in preparation for introducing, in the accompanying Part II, the “High-Order Function/Feature Adjoint Sensitivity Analysis Methodology” (nth-FASAM), which aims at most efficiently computing exact expressions of high-order sensitivities of model responses to functions (“features”) of model parameters.

Conceptual design of megawatt-level mobile nuclear power system based on heat pipe cooled reactor

Mobile nuclear power system has the advantages such as the well adaptability, the strong sustainability, and the convenient transportation, which can satisfy the energy demand of special environments such as island, and polar region. In this paper, the conceptual design of Mobile Nuclear Power System named MNPS-1000 is proposed, which is consist of the modular heat pipe cooled reactor and combined cycle energy conversion system to achieve the 1MWe output. The design characteristics include the operation lifetime of 3000 days in full power mode, negative temperature reactivity feedback, redundancy in reactivity control, 33% energy conversion efficiency. Due to the efficient heat transfer capability of lithium heat pipes, total of 216 heat pipes can ensure the heat transfer of 3MWt. The modular design of reactor and heat pipe heat exchanger decreases the volume of the system to achieve the compact arrangement in the standard containers with 12.0m×2.5m×2.5m size. The reactor physics and thermal hydraulics analysis, heat pipe design, and energy conversion system analysis are taken out to show the feasibility and performances of this conceptual design.

Results of Experiments under the Physical Start-Up Program of the IVG.1M Reactor

In 2022, the physical start-up stage of the IVG.1M research reactor was successfully completed, initiated by reducing the fuel enrichment of 235U. This phase included the loading of nuclear fuel into the reactor core and conducting experiments to determine the neutron-physical characteristics of the reactor. Prior to the physical start-up, preliminary calculations were performed using the computational code MCNP6 and a full-scale model of the IVG.1M reactor with low-enriched uranium fuel (LEU). During the start-up series, the reactivity worth curves of the reactor control and protection system’s operating and compensating elements were determined. Additionally, experiments were performed to measure the reactivity effects of technological channel draining and to obtain activation reaction rates in the central experimental channel using nickel and gold activation indicators. The results of determining the neutron-physical characteristics of the IVG.1M reactor have confirmed the operability of the reactor core with LEU fuel.

Temperature Control of a Chemical Reactor Based on Neuro-Fuzzy Tuned with a Metaheuristic Technique to Improve Biodiesel Production

This work deals with the problem of choosing a controller for the production of biodiesel from the transesterification process through temperature control of the chemical reactor, from the point of view of automatic control, by considering such aspects as the performance metrics based on the error and the energy used by the controller, as well as the evaluation of the control system before disturbances. In addition, an improvement method is proposed via a neuro-fuzzy controller tuned with a metaheuristic algorithm to increase the efficiency of the chemical reaction in the reactor. A clear improvement is shown in the minimization of the integral of time multiplied squared error criterion (ITAE) performance index with respect to the proposed method (8.1657 ×104) in relation to the PID controller (7.8770 ×107). Moreover, the integral of the total control variation (TVU) performance index is also shown to evaluate the power used by the neuro-fuzzy controller (25.7697), while the PID controller obtains an index of (32.0287); this metric is especially relevant because it is related to the functional requirements of the system since it quantifies the variations of the control signal.

An outline of high-fidelity neutron transport simulations for advanced nuclear reactor concepts

Development of new reactor concepts to suit future requirements and safety standards, needs very accurate and efficient reactor simulations and analysis. This necessitates development of high fidelity reactor physics computer codes. The present paper outlines various physics design tools being developed for the core design of advanced reactor concepts such as High Temperature Reactor (HTR) and Molten Salt Reactor (MSR) etc. Modelling advancements to analyze complex features unique to new reactor designs are also discussed in brief.

Model-Based Fault Diagnosis and Fault Tolerant Control for Safety-Critical Chemical Reactors: A Case Study of an Exothermic Continuous Stirred-Tank Reactor.

In safety-critical chemical reactors with potential hazards, reaction kinetics and heat transfer parameters are usually known, and a mathematical model is available. It is then meaningful to base fault detection and isolation algorithms on the first-principles model as opposed to statistics, so that physically meaningful residual signals are generated from material and/or energy balances not closing, leading to reliable fault diagnosis. Additionally, to maintain the safety of the entire system, it is necessary to take appropriate control action based on the mathematical model and the identified faults, to minimize their impact and thus ensure safe operation. In the present work, these ideas will be formulated and illustrated through a continuous stirred-tank reactor case study involving the liquid-phase oxidation of alkylpyridine with hydrogen peroxide. The proposed fault tolerant control strategy monitors the DSM (distance of the system state from the boundary of the dynamic safe set) and the estimate of the fault size, and when they cross a certain limit as a result of an abnormal event, the manipulated input is switched. Simulation results show the effectiveness of the proposed fault tolerant control strategy in dealing with cooling system failure.

Modeling and simulation of neutron noise triggered by fuel assembly vibrations in 3D hexagonal geometry

Neutron noise is a natural phenomenon in nuclear reactors. Hence, its investigation plays a significant role in nuclear reactor physics and safety-related issues. While neutron noise could have various origins, the proposed work focuses on those induced by fuel assembly vibration in hexagonal cores. To this aim, a 3D neutron noise simulator has been developed based on the multi-point kinetics equations for a hexagonal geometry coupled with the expanded multi-nodal approach as a thermal-hydraulic model. Employing these models, the neutron noise was analyzed in the time domain to provide the advantage of modeling non-linearities. This simulator is capable of simultaneous simulation of vibrating fuel assemblies with various vibrational characteristics, in particular, mode. It features the capability of neutron noise modeling at both the nuclear data generation level and the level of the neutronic calculations. The validity of the model is demonstrated by a transient accident and a noise problem. The outcomes are compared to reference data, showing good agreement. Then, to further study noise responses, several scenarios encircling various vibrating fuel assemblies in different situations are simulated. These experiments prove the appropriate performance of the proposed simulator for modeling and analyzing neutron noise in hexagonal cores.

Benchmarking exercise of indigenous Monte Carlo neutron transport code PATMOC for hexagonal full core reactor geometry

An indigenous Monte Carlo neutron transport code, named PATMOC, has been designed and developed at Bhabha Atomic Research Centre (BARC) for reactor physics design applications. The code has been extensively tested for its algorithmic accuracy against numerous international numerical benchmarks, has also been validated on practical nuclear reactor systems like Advanced Heavy Water Reactor Critical Facility (AHWR-CF) and Apsara-U pool type research reactor located at BARC, and is now in regular use for day-to-day reactor physics studies. These reactor systems and most of the benchmark problems used for the verifications and validation of the code have square lattice arrangement in the core. In this paper, we present the results of verification of PATMOC code on whole-core reactor system with hexagonal lattice arrangement of fuel elements. In this exercise, we have analyzed the High Temperature engineering Test Reactor (HTTR) whole-core benchmark for integral and differential parameters at both lattice and core level. The results demonstrate the algorithmic accuracy of the code on hexagonal reactor systems also. This exercise will help make use of this code for reactor physics design studies also for the reactor systems with hexagonal arrangement.

A Review of Candidates for a Validation Data Set for High-Assay Low-Enrichment Uranium Fuels

Many advanced reactor concept designs rely on high-assay low-enriched uranium (HALEU) fuel, enriched up to approximately 19.75% 235U by weight. Efforts are underway by the US government to increase HALEU production in the United States to meet anticipated needs. However, very few data exist for validation of computational models that include HALEU, beyond a few fresh fuel benchmark specifications in the International Reactor Physics Experiment Evaluation Project. Nevertheless, there are other data with potential value available for developing into quality benchmarks for use in data- and software-validation efforts. This paper reviews the available evaluated HALEU fuel benchmarks and some of the potentially relevant benchmarks for fresh highly enriched uranium. It then introduces experimental data for HALEU fuel irradiated at Idaho National Laboratory, from relatively recent irradiation programs at the Advanced Test Reactor. Such data should be evaluated and, if valuable, collected into detailed benchmark specifications to meet the needs of HALEU-based reactor designers.

Online training and education from the VR-1 reactor—Lessons learned

Hands-on education and training is a key part of fixing and developing technology knowledge and is an inherent part of many engineering and scientific curricula. However, access to large complex training facilities, such as nuclear reactor, could be limited by various factors, such as unavailability of those facilities in the region, high traveling costs or harmonization of the schedules of hands-on E&T with theoretical lectures and with the operational schedule of the facility. To handle the issue, several success stories have been reached with the introduction of the Internet Reactor Labs (IRL). The Internet Reactor Labs can strongly contribute to accessibility of training at research reactors and can contribute to improvements in their utilization. The paper describes the development of the Internet Reactor Lab at the VR-1 reactor of the Czech Technical University in Prague. Contrary to single-purpose IRLs, it presents various modalities of online teaching and training in experimental reactor physics and reactor operation in general as well as outreach activities that have been developed in recent years.

Analysis of Kobayashi benchmark with indigenous Monte Carlo neutron transport code PATMOC

The solution of the neutron transport equation is the basic input for the reactor physics design of a nuclear reactor system. Because of the complexities of geometry and cross-section data, the neutron transport equation is generally solved using numerical methods. One of the difficulties in the solution using these methods concerns the accuracy of distribution of neutron flux in the system containing void regions in a highly absorbing medium. The difficulty arises because of the issue in the continuity of flux at the void and material interface. There is a sudden and large change in the flux at this interface. Kobayashi benchmarks are widely used problems for testing the ability and accuracy of reactor physics codes to compute neutron flux distribution on such systems. An indigenous Monte Carlo neutron transport code, named PATMOC, has been designed and developed at Bhabha Atomic Research Centre (BARC) for reactor physics design applications. The Kobayashi benchmarks have been used to test the PATMOC code to verify its accuracy in flux computation for systems with voids in-between high absorbing materials. Our results show that the PATMOC estimated values of flux distribution in the system compare very well with the reference results provided with the benchmark. In this paper we present the detailed results and analyses of this benchmark with PATMOC code.

Machine learning-based predictive control using on-line model linearization: Application to an experimental electrochemical reactor

The electrochemical reaction-based process, a new type of chemical process that can generate valuable products using renewable electricity, is a sustainable alternative to the traditional chemical manufacturing processes. One promising research area of electrochemical reaction processing is to reduce carbon dioxide (CO2) into carbon-based products, which can contribute to closing the carbon cycle if CO2 is directly captured from the atmosphere. In this work, we demonstrate a model predictive control (MPC) scheme that uses a neural network (NN) model as the process model to implement real-time multi-input-multi-output (MIMO) control in an electrochemical reactor for CO2 reduction. Specifically, a long short-term memory network (LSTM) model is developed using historical experimental data of the electrochemical reactor to capture the nonlinear input-output relationship as an alternative to the complex, first principles-based model. Furthermore, the Koopman operator method is used to linearize the LSTM model to reduce the nonlinear optimization step in the MPC to a well-understood and easy-to-solve quadratic programming (QP) problem. The performance of the LSTM model, Koopman-based optimization, and MPC using the linearization of the LSTM model are evaluated with various simulations as well as open-loop and closed-loop experiments. As the results, the proposed MPC scheme can drive the two output states, that are concentrations of the products (C2H4 and CO), to their desired setpoints by computing optimal input variables (surface potential and electrode rotation speed) in real-time in closed-loop experiments. Furthermore, a transfer learning-based method is utilized to update the NN model to handle process variability.

Research on Solid Oxide Fuel Cell System Model Building and 3D Testing Based on the Nodal Idea

The Solid Oxide Fuel Cell (SOFC) system is a highly intricate system characterized by multiple variables and couplings. Developing an accurate model for the SOFC independent power generation system is of paramount importance. Conducting experimental studies on the SOFC system is costly, and it carries certain risks due to the requirements for pure hydrogen, high-temperature environments, and other factors. To address these challenges, a high-performing model that precisely reflects the inherent characteristics of the SOFC is essential for dynamic static analysis and the identification of optimal operating points. This paper presents a SOFC system model based on current controls, which was implemented in the MATLAB/Simulink environment, and it utilized a nodal approach for modeling. The model incorporated a cold air bypass, which enabled the more precise control of the SOFC reactor’s inlet and outlet temperatures. Furthermore, a 3D test and verification method are proposed in order to focus on the influence of input parameters on the four electrical characteristics, and four thermal characteristics, of output parameters. By conducting one-dimensional, two-dimensional, and three-dimensional studies of these output parameters, a more intuitive understanding of the system’s response to changes in input parameters was obtained. Under conditions wherein all other variables were kept constant, the entire system attained its maximum efficiency at approximately FU = 0.8, BP = 0, and AR = 6. The outcomes of this study have significant implications for exploring the optimal operating point in the SOFC independent power generation system in an in-depth manner. It provides valuable insights for enhancing the system’s efficiency and performance.

Revolutionizing LWR SMR reactors: exploring the potential of (Th-233U-235U)O2 fuel through a parametric study

ABSTRACT Small modular reactors (SMRs) have garnered significant attention for their operational adaptability and ease of deployment. Thorium, with its well-documented advantages, shows promise as a viable fuel option for SMRs. However, the absence of intrinsic fissile components in thorium necessitates the exploration of different thorium-based fuel combinations. One such combination, (Th-233U)O2 fuel, has limitations due to the presence of pure U-233. To overcome this challenge, a new fuel mixture, (Th-233U-235U)O2, was investigated for SMRs. This study examined the reactor physics characteristics of the (Th-233U-235U)O2 fuel, including fuel burnup, neutron flux spectra, power distribution, the evolution of actinides, and reactivity coefficients. Results indicate that the (Th-233U-235U)O2 fuel allows for a longer criticality period compared to UO2 fuel, with up to a 14% improvement, while accumulating fewer plutonium and transuranic elements. Notably, it demonstrates significantly improved negative reactivity coefficients, particularly for moderator temperature, with an average improvement of 45% over (Th-233U)O2 fuel. The conceptual (Th-233U-235U)O2 fuel, therefore, exhibits promising neutronic properties, presenting possibilities for future studies. These findings contribute to the understanding and advancement of advanced fuel designs for SMRs.