Advanced nuclear reactors hold strong potential for clean and safe energy production. From the various designs, high-temperature gas-cooled reactors (HTGRs) are among the most promising ones. One fundamental aspect for their safety evaluation is the uncertainty quantification (UQ) of HTGR models. This study introduces a UQ framework developed around the VSOP code system. The framework uses the DAKOTA statistical toolkit to sample various case-dependent inputs, such as manufacturing parameters and boundary conditions. A Python driver script is developed to create an interface between DAKOTA and VSOP. Dedicated sampling modules are developed for perturbing the case-independent inputs that include: background microscopic cross sections, fission yields, decay constants, and resonance integral parameters. The capabilities of the UQ framework are demonstrated on an 80-MW(thermal) pebble-bed small modular reactor equilibrium core model. Four different UQ studies are performed to understand and quantify the impact of various sets of inputs. Initially, perturbations in the cross sections are analyzed, given their inherent complex nature. The results show that the predicted k(eff) uncertainty is similar to 420 pcm, a value consistent with those reported in the literature for pebble-bed reactors. The most statistically significant cross sections are the U-235 number of average neutrons per fission, the U-235 and Pu-239 fission, and the U-235 and Pu-239 capture in thermal energies. Small uncertainties are obtained for the maximum burnup and fuel temperature, with values less than 0.15%. The second study assessed the additional impact of the fission yields and decay constants. The results show an impact of 50 pcm on the k(eff), with a negligible impact on the other outputs of interest. The third study involved the perturbation of all the inputs, which resulted in unrealistically large uncertainties to most outputs due to the fuel kernel radius. This is attributed to the VSOP limitations for such uncertainty studies, since individual fuel kernels cannot be explicitly modeled, requiring the same fuel kernel radius perturbation to be applied in every coated particle for all fuel pebbles of the core. A more realistic approach is discussed and investigated in the fourth study. The results show that the cross sections remain the most important contributors for the k(eff), the thermal flux distribution, and the power density distribution. However, for the maximum burnup, the maximum fuel temperature, and the gas temperature distribution, the power and mass flow rate boundary conditions are the most statistically significant inputs. Future work will aim to further refine and expand the VSOP UQ framework, and to perform code-to-code uncertainty comparison studies for different HTGR cores, such as the PBMR-400.

The advanced thermal-hydraulics sub-channel tool CTF has been in the process of continuous development and improvement by Oak Ridge National Laboratory (ORNL) and North Carolina State University (NCSU). In recent years, there has been considerable progress in code development, including new functionalities, application-specific correlations, various multi-physics applications, built-in pre- and post-processors, improved solvers, parallelization, and extensive testing. VVER applications are part of these activities. NCSU has been cooperating with the Institute for Nuclear Research and Energy (INRNE) on CTF development, verification, and validation for VVER core modeling and simulation. This article presents an overview of these CTF studies for VVER applications. Several test cases are considered, which include pure thermal-hydraulic problems as well as multi-physics simulations at the nodal and pin level. On the single physics side, thermal-hydraulic CTF solutions have been compared against measured data for rod bundle, fuel assembly, and full core, as well as code-to-code vs. FLICA4 solutions. CTF was tested in the simulation of the TVSA-5T VVER mini-assembly experiments and in the full-core steady-state calculation for the ongoing OECD/NEA Rostov-2 benchmark. For the TVSA-5T calculations, CTF was coupled with the uncertainty analysis tool Dakota and utilized to propagate uncertainties of input and boundary conditions to output quantities of interest for thermal-hydraulic parameter investigations. The CTF results and measured data obtained from this experimental setup were compared for validation. To produce reliable pin-resolved reference solutions for multi-physics model testing the high-fidelity continuous energy Monte Carlo-based neutron transport codes MCNP6.2 and Serpent 2.2.0 were separately coupled with the CTF sub-channel code. Coupled models of a VVER-1000 fuel assembly were tested in comparisons between MCNP/CTF and Serpent/CTF results. Coarse-mesh multi-physics solutions for a full core have been obtained with the coupled COBAYA/CTF, COBAYA/FLICA4, and PARCS/CTF codes. These solutions have been compared against steady-state plant data and code-to-code for transients. High-fidelity pin-resolved solutions with SERPENT/CTF serve as reference solutions in a steady state. The outcomes from the various studies of single-physics and multi-physics cases used for CTF verification and validation met the initial expectations both qualitatively and quantitatively. The results of the numerical verification and experimental validation are in good agreement with the corresponding reference data.

This study aims to develop and verify the multi-physics high-resolution coupled code system nTRACER/CTF for full core depletion calculations in Cartesian geometry. The verifications are conducted on the basis of the OECD/ NEA TVA Watts Bar 1 benchmark (TVA WB1), using multi-physics high-resolution results from the Virtual Environment for Reactor Applications (VERA), which includes MPACT and CTF. The paper presents the development of the nTRACER/CTF coupled system for depletion calculations in PWRs, which are based on the Cartesian geometry. The nTRACER/CTF model is verified under the Hot Zero Power Condition (HZP) at the beginning of the first cycle and the HFP case of TVA WB1. The Critical Boron Concentration (CBC) differences are less than 17 ppm in both cases, while the RMS differences in pin-wise power distributions are less than 0.7 % in both cases. The impacts of discrepancies between the nTRACER/CTF and VERA models are also quantified. nTRACER/CTF depletion calculations are performed for the full first cycle of TVA WB1 according to the simplified power curve presented in the benchmark specifications. The system is verified with VERA results for every burnup step of the cycle, in terms of CBC, axially averaged pin power distribution, outlet temperature distribution and axial power profile. The RMS of CBC differences after achieving a full power condition is 25 ppm. The RMS differences in pin-wise power and outlet temperature distributions are less than 1.12 % and 0.4 degrees C, which are within the target accuracies of 1.5 % and 2 degrees C for all depletion steps.

This paper shows models developed and results obtained for neutronics simulations of the 3D core of C5G7-TD Benchmark using the Serpent code, and an approach for multi-physics coupling for Serpent/CTF codes was presented. Neutronic simulations included control rod movements and moderator density changes, showing good Serpent results when compared to other codes. Future efforts will include the multi-physics simulation of the transients included in Phase II of the Benchmark.

The International Atomic Energy Agency recently concluded a Coordinated Research Program (CRP) to evaluate the effect of propagation of uncertainties on design and safety parameters in High Temperature Gas-cooled Reactors (HTGRs). This CRP catalyzed the development of novel software and methods relevant to HTGR uncertainty analysis. In the framework of this CRP, the statistical analysis code RAVEN was coupled to the neutron transport code PHISICS, using 6-group cross section libraries generated with the modules TRITON/NEWT from SCALE 6.2.1. This article describes the mechanics of the RAVEN/PHISICS sequence, and reports the effects of manufacturing uncertainties on integral parameter uncertainties found in the Very High Temperature Reactor Critical (VHTRC) core. The VHTRC experimental results included propagation of manufacturing uncertainties to obtain eigen-value (keff) and temperature coefficient (alpha(T)) uncertainties. RAVEN/PHISICS was used to reproduce this analysis and to compare the predicted output uncertainties to the experimental measurements on the three VHTRC cores (HC-I, HP, HC-II). Results from the sequence agree with the experimental values (sigma [keff] similar to 0.00300). The analysis also focuses on the interpretation of input uncertainties. The simulations conducted with RAVEN/PHISICS demonstrated the input uncertainties can induce a threefold increase in the resulting output uncertainties, depending on the mathematical modeling of the raw input uncertainties. In particular, the use of a unique uncertainty value repeated over lattice elements constitutes the major contribution to the keff and aT uncertainties, while modeling these uncertainties with random independent values leads to negligible keff and aT uncertainties, due to cancellation of errors. The propagation of the manufacturing uncertainties was also repeated using 56 energy groups in the neutron transport calculations, and showed a moderate impact on the output (keff, aT) uncertainties (similar to 10 % difference) compared to the base-case 6-group simulations. (C) 2021 Elsevier Ltd. All rights reserved.

The Nearly Autonomous Management and Control System (NAMAC) is a comprehensive control system that assists plant operations by furnishing control recommendations to operators in a broad class of situations. This study refines a NAMAC system for making reasonable recommendations during complex loss-of-flow scenarios with a validated Experimental Breeder Reactor II simulator, digital twins improved by machine-learning algorithms, a multi-attribute decision-making scheme, and a discrepancy checker for identifying unexpected recommendation effects. We assessed the performance of each NAMAC component, while we demonstrated and evaluated the capability of NAMAC in a class of loss-of-flow scenarios.

Best Estimate Plus Uncertainty (BEPU) approaches for nuclear reactor applications have been extensively developed in recent years. The challenge for BEPU approaches is to achieve multi-physics modeling with an acceptable computational cost while preserving a reasonable fidelity of the physics modeled. In this work, we present the core multi-physics computational framework developed for the efficient computation of uncertainties in Light Water Reactor (LWR) simulations. The subchannel thermal-hydraulic code CTF and the nodal expansion neutronic code PARCS are coupled for the multi-physics modeling (CTF-PARCS). The computational framework is discussed in detail from the Polaris lattice calculations up to the CTF-PARCS coupling approaches. Sampler is used to perturb the multi-group microscopic cross-sections, fission yields and manufacturing parameters, while Dakota is used to sample the CTF input parameters and the boundary conditions. Python scripts were developed to automatize and modularize both pre- and post-processing. The current state of the framework allows the consistent perturbation of inputs across neutronics and thermal-hydraulics modeling. Improvements to the standard thermal-hydraulics modeling for such coupling approaches have been implemented in CTF to allow the usage of 3D burnup distribution, calculation of the radial power and the burnup profile, and the usage of Santamarina effective Doppler temperature. The uncertainty quantification approach allows the treatment of both scalar and functional quantities and can estimate correlation between the multi-physics outputs of interest and up to the originally perturbed microscopic cross-sections and yields. The computational framework is applied to three exercises of the LWR Uncertainty Analysis in Modeling Phase III benchmark. The exercises cover steady-state, depletion and transient calculations. The results show that the maximum fuel centerline temperature across all exercises is 2474K with 1.7% uncertainty and that the most correlated inputs are the 238U inelastic and elastic cross-sections above 1 MeV.

This paper develops a Nearly Autonomous Management and Control (NAMAC) system for advanced reactors. The development process of NAMAC is characterized by a three layer-layer architecture: knowledge base, the Digital Twin (DT) developmental layer, and the NAMAC operational layer. The DT is described as a knowledge acquisition system from the knowledge base for intended uses in the NAMAC system. A set of DTs with different functions is developed with acceptable performance and assembled according to the NAMAC operational workflow to furnish recommendations to operators. To demonstrate the capability of the NAMAC system, a case study is designed, where a baseline NAMAC is implemented for operating a simulator of the Experimental Breeder Reactor II during a single loss of flow accident. When NAMAC is operated in the training domain, it can provide reasonable recommendations that prevent the peak fuel centerline temperature from exceeding a safety criterion.

In recent years, large efforts have been devoted to Light Water Reactor (LWR) Uncertainty Quantification (UQ). In 2006, the LWR Uncertainty Analysis in Modeling (UAM) benchmark was launched with an aim to investigate the uncertainty propagation in all modeling stages of the LWRs and guide uncertainty and sensitivity analysis methodology development. This article summarizes the benchmark activities for the standalone neutronics phase (Phase I), which includes three main exercises: Exercise I-1: "Cell Physics," Exercise I-2: "Lattice Physics," and Exercise I-3: "Core Physics." A comparative analysis of the Phase I results is performed in this article for all the considered LWRs types: Three Mile Island - 1 Pressurized Water Reactor (PWR), Peach Bottom - 2 Boiling Water Reactor (BWR), Kozloduy - 6 Water - Water Energetic Reactor (VVER) and a Generation-III reactor. It was found, for all major exercises, that the predicted uncertainty of the system eigenvalue is highly dependent on the choice of the covariance libraries used in the UQ process and is less sensitive to the solution method, nuclear data library and UQ method. For all four reactor types, the observed relative standard deviation across all exercises is approximately 0.5% for the UO2 fuel. In the pin cell and lattice calculations with MOX fuel this uncertainty increases to 1%. The main reason is the larger Pu-239 nu-bar uncertainty compared to the U-235 nu-bar. The largest contributors to the eigenvalue uncertainties are the U-235 nu-bar and the U-238 capture in the UO2 fuel and the Pu-239 nu-bar in the MOX fuel. In the assembly lattice exercises, higher uncertainties are predicted for the fast group than the thermal group constants with differences up to one order of magnitude. This is attributed to the larger uncertainties of most cross-sections at high energies. The obtained correlation matrices share some common major trends but also exhibit strong differences in case by case comparisons indicating an impact of the selected neutronics modeling and nuclear data library. In the core exercises, the predicted relative standard deviation of the radial and axial power, for most of the cores, is below 10%. An exception is the radial power profile of the Generation-III core, when a mixture of UOX/MOX assemblies is considered. Finally, it is important to note that the bias in most of the studies is significant and up to the same order of the estimated uncertainty. This indicates a need for better quantification of the bias/variance through more code to code and code to experiments comparisons.

A critical component of the autonomous control system is the implementation of digital twin (DT) for diagnosing the conditions and prognosing the future transients of physical components or systems. The objective is to achieve an accurate understanding and prediction of future behaviors of the physical components or systems and to guide operating decisions by an operator or an autonomous control system. With specific requirements in the functional, interface, modeling, and accuracy, DTs are developed based on operational and simulation databases. As one of the modeling methods, data-driven methods have been used for implementing DTs since they have more adaptive forms and are able to capture interdependencies that can be overlooked in model-based DTs. To demonstrate the capabilities of DTs, a case study is designed for the control of the EBR-II sodium-cooled fast reactor during a single loss of flow accident, where either a complete or a partial loss of flow in one of the two primary sodium pumps is considered. Based on the definition of DTs and the design of autonomous control system, DTs for diagnosis and prognosis are implemented by training feedforward neural networks with suggested inputs, training parameters, and knowledge base. Furthermore, inspired by the validation and uncertainty quantification scheme for scientific computing, a list of sources of uncertainty in input variables, training parameters, and knowledge base is formulated. The objective is to assess qualitative impacts of different sources of uncertainty on the DT errors. It is found that the performance of DT for diagnosis and prognosis satisfies the acceptance criteria within the training databases. Meanwhile, the accuracy of DTs for diagnosis and prognosis is highly affected by multiple sources of uncertainty.

In this work, a Nearly Autonomous Management and Control (NAMAC) system is designed to diagnose the reactor state and provide recommendations to the operator for maintaining the safety and performance of the reactor. A three layer-hierarchical workflow is suggested to guide the design and development of the NAMAC system. The three layers in this workflow corresponds to knowledge base, digital twin developmental layer (for different NAMAC functions), and NAMAC operational layer. Digital twin in NAMAC is described as knowledge acquisition system to support different autonomous control functions. Therefore, based on the knowledge base, a set of digital twin models is trained to determine the plant state, predict behavior of physical components or systems, and rank available control options. The trained digital twin models are assembled according to NAMAC operational workflow to support decision-making process in selecting the optimal control actions during an accident scenario. To demonstrate the capability of the NAMAC system, a case study is designed, where a baseline NAMAC is implemented for operating a simulator of the Experimental Breeder Reactor II (EBR-II) during a single loss of flow accident. Training database for development of digital twin models is obtained by sampling the control parameters in the GOTHIC data generation engine. After the training and testing, the digital twins are assembled into a NAMAC system according to the operational workflow. This NAMAC system is coupled with the GOTHIC plant simulator, and a confusion matrix is generated to illustrate the accuracy and robustness of implemented NAMAC system. It is found that within the training databases, NAMAC can make reasonable recommendations with zero confusion rate. However, when the scenario is beyond the training cases, the confusion rate increases, especially when the scenarios are more severe. Therefore, a discrepancy checker is added to detect unexpected reactor states and alert operators for safety-minded actions.

Transient calculations with nodal neutronics codes entail few-group energy structures. In systems other than LWRs, significant efforts are devoted to obtain satisfying group structures. The energy cut-offs available in the literature do not always match the energy boundaries available in lattice codes. This paper demonstrates an automated sequence that searches for suitable coarse-group configurations. The sequence couples the lattice code T-XSEC/NEWT for cross section generation and collapsing, the nodal code PHISICS for core calculations and the software RAVEN for variable sampling and analytical purposes. T-XSEC/NEWT receives an energy group configuration from RAVEN to generate microscopic self-shielded cross sections in a coarse format. PHISICS provides the core solution using the microscopic libraries. The performances of the group structures in the core model are stored to train a Reduced Order Model (ROM) built on-the-fly. The ROM spares the necessity to survey the large input space of all possible energy group structures, or expert judgements. The solution provided by RAVEN is a Limit Surface of group structures fitting success criteria. The approach is tested on a simplified two-dimensional HTTR core model. The Limit Surface obtained by RAVEN derives a few six-group structures fitting the HTTR model.

Uncertainty and sensitivity analysis is an indispensable element of any substantial attempt in reactor simulation validation. A Coordinated Research Program (CRP) supervised by the International Atomic Energy Agency was started to investigate the various uncertainty quantification methodologies for High Temperature Gas-cooled Reactors. The first phase of the CRP is dedicated to the estimation of cell and lattice model uncertainties due to the neutron cross sections. Phase II is oriented towards the investigation of propagated uncertainties from the lattice to the coupled neutronics/thermal hydraulics core calculations. Best-estimate results for the prismatic single block (Ex. I-2a) and super cell models (Ex. I-2c) were obtained using the SCALE 6.2.0 two-dimensional lattice code NEWT. A reference spectrum was obtained with Serpent 2.1.27 for the single block, super cell and core models. The flux spectrum in the system of interest plays a primary role in the quantification of uncertainties caused by cross sections. In this work, the TRITON/NEWT-flux-weighted cross sections obtained for Ex. I-2a and various models of Ex.I-2c are utilized to perform a sensitivity analysis of the MHTGR-350 core power densities and eigenvalues. The core solutions are obtained with the Idaho National Laboratory (INL) coupled code PHISICS/RELAP5-3D. It is observed that axial shape of the core power density does not vary significantly with the various lattice cell libraries utilized. The use of cross section libraries originating from super cells induces changes of the core power density by 1–10% radially as compared to the Ex.I-2a cross sections. The magnitude of these variations increases as the moderator-to-fuel ratio increases in the super cell lattice models. A lattice flux spectrum resembling the core spectrum is hence necessary for correct predictions in nodal core calculations.

Best-estimate plus uncertainty analysis of reactors is replacing the traditional conservative (stacked uncertainty) method for safety and licensing analysis. To facilitate uncertainty analysis applications, a comprehensive approach and methodology must be developed and applied. High temperature gas cooled reactors (HTGRs) have several features that require techniques not used in light-water reactor analysis (e.g., coated-particle design and large graphite quantities at high temperatures). The International Atomic Energy Agency has therefore launched the Coordinated Research Project on HTGR Uncertainty Analysis in Modeling to study uncertainty propagation in the HTGR analysis chain. The benchmark problem defined for the prismatic design is represented by the General Atomics Modular HTGR 350. The main focus of this report is the compilation and discussion of the results obtained for various permutations of Exercise I 2c and the use of the cross section data in Exercise II 1a of the prismatic benchmark, which is defined as the last and first steps of the lattice and core simulation phases, respectively. The report summarizes the Idaho National Laboratory (INL) best estimate results obtained for Exercise I 2a (fresh single-fuel block), Exercise I 2b (depleted single-fuel block), and Exercise I 2c (super cell) in addition to the first results of an investigation into the cross section generation effects for the super-cell problem. The two dimensional deterministic code known as the New ESC based Weighting Transport (NEWT) included in the Standardized Computer Analyses for Licensing Evaluation (SCALE) 6.1.2 package was used for the cross section evaluation, and the results obtained were compared to the three dimensional stochastic SCALE module KENO VI. The NEWT cross section libraries were generated for several permutations of the current benchmark super-cell geometry and were then provided as input to the Phase II core calculation of the stand alone neutronics Exercise II 1a. The steady state core calculations were simulated with the INL coupled-code system known as the Parallel and Highly Innovative Simulation for INL Code System (PHISICS) and the system thermal-hydraulics code known as the Reactor Excursion and Leak Analysis Program (RELAP) 5 3D using the nuclear data libraries previously generated with NEWT. It was observed that significant differences in terms of multiplication factor and neutron flux exist between the various permutations of the Phase I super-cell lattice calculations. The use of these cross section libraries only leads to minor changes in the Phase II core simulation results for fresh fuel but shows significantly larger discrepancies for spent fuel cores. Furthermore, large incongruities were found between the SCALE NEWT and KENO VI results for the super cells, and while some trends could be identified, a final conclusion on this issue could not yet be reached. This report will be revised in mid 2016 with more detailed analyses of the super-cell problems and their effects on the core models, using the latest version of SCALE (6.2). The super-cell models seem to show substantial improvements in terms of neutron flux as compared to single-block models, particularly at thermal energies.