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Sodium-cooled fast reactor (SFR) technologies have the potential to guarantee energy supply and to reduce the burden of nuclear waste for future generations. For an adequate simulation of these reactor systems, well-established tools that have so far been applied mainly to light water reactor (LWR) concepts need to be validated and enhanced. For li...
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The MIT BEAVRS benchmark problem, which was primarily setup for the verification and validation of high-fidelity tools that have coupled neutron transport, thermal-hydraulics, and fuel isotopic depletion models, has also found extensive usage in the reactor physics community for validating core analysis tools. The primary purpose of this paper is t...
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... Neutron transport simulations inherently have numerical and modeling approximations leading to uncertainties (Wieselquist et al., 2020). Although these uncertainties may introduce a noticeable uncertainty, for example, from a multigroup approximation (Bostelmann, 2020;Ternovykh and Bogdanova, 2020;Zwermann et al., 2020), nuclear data are evidently a substantial source of uncertainties too as a basis for every transport simulation (Nikolaev, 2013). Inasmuch as nuclear data come from measurements and the following evaluation, they have a certain level of uncertainties with corresponding covariance data due to energy, reaction, and material correlations. ...
... There are eigenvalues, cross sections, and reactivity effects among these responses. A number of results has been already published applying different codes, for example, UNICORN (Qiao et al., 2019), SCALE (Bostelmann, 2020;Zwermann et al., 2020), and MCS (Jo et al., 2021). In addition, there are works concerned with SFRs unrelated to the benchmark (García-Herranz et al., 2017;Zheng et al., 2018;Ma et al., 2021;Romojaro et al., 2021;Rivas et al., 2022). ...
... In this work, two models of SFRs, which are briefly mentioned in Section 1, are considered: MET1000 with metallic fuel and MOX3600 with MOX fuel (Bostelmann, 2020). ...
Thermal-spectrum molten salt reactor (MSR) concepts usually adopt graphite as a neutron moderator. Although graphite as a moderator has many advantages, it also has drawbacks, including a relatively short lifespan (it has to be replaced), positive temperature feedback, and loss of impermeability due to expansion. Replacing graphite with heavy water in MSRs can effectively solve the problems introduced by graphite. The SD-HWMSR is a Single-fluid Double-zone Heavy Water-moderated Molten Salt Reactor. Optimization of SD-HWMSR’s fuel channel pitch and radius has been conducted in this work. As a result, the SD-HWMSR with a high breeding ratio (1.07465 ± 0.00060), low initial 233U loading (1.43
), and negative temperature and void reactivity coefficients is put forward. The SERPENT-2 is used to analyze the neutronics parameters of the reactor design. The current work investigates the change in the multiplication factor, breeding ratio, and the accumulation of significant nuclides in the core. The suitable 232Th and 233U refill rates needed to maintain criticality and enable analysis of the whole core of SD-HMMSR are thoroughly determined in this study. Uranium-233 and thorium-232 both have a maximum refill rate of 3.49 and 3.20
, respectively. While the average refill rate for 233U and 232Th during the 60 years of operation is 1.90 and 2.35
, respectively. The net production of 233U rises with time, and by the end of the 60 years, it is around 1.98
. The doubling time for the SD-HWMSR is 31
, which is consistent with previous results.
... Neutron transport simulations inherently have numerical and modeling approximations leading to uncertainties (Wieselquist et al., 2020). Although these uncertainties may introduce a noticeable uncertainty, for example, from a multigroup approximation (Bostelmann, 2020;Ternovykh and Bogdanova, 2020;Zwermann et al., 2020), nuclear data are evidently a substantial source of uncertainties too as a basis for every transport simulation (Nikolaev, 2013). Inasmuch as nuclear data come from measurements and the following evaluation, they have a certain level of uncertainties with corresponding covariance data due to energy, reaction, and material correlations. ...
... There are eigenvalues, cross sections, and reactivity effects among these responses. A number of results has been already published applying different codes, for example, UNICORN (Qiao et al., 2019), SCALE (Bostelmann, 2020;Zwermann et al., 2020), and MCS (Jo et al., 2021). In addition, there are works concerned with SFRs unrelated to the benchmark (García-Herranz et al., 2017;Zheng et al., 2018;Ma et al., 2021;Romojaro et al., 2021;Rivas et al., 2022). ...
... In this work, two models of SFRs, which are briefly mentioned in Section 1, are considered: MET1000 with metallic fuel and MOX3600 with MOX fuel (Bostelmann, 2020). ...
... XSUSA can calculate indices based on correlations of nuclear data perturbations with the output to estimate the importance of the individual nuclide reactions for the output uncertainty (Bostelmann et al., 2018). The calculation of Sobol' main effect and total effect sensitivity indices was previously demonstrated and shown to provide almost consistent results with these correlation indices (Bostelmann, 2020). Other codes that use the random sampling approach for nuclear data uncertainty analysis are the PSI codes SHARK-X (Wieselquist et al., 2013), the Sandia National Laboratory code DAKOTA (Swiler et al., 2018) and NUSS (Zhu et al., 2015), as well as the fast Total Monte Carlo (TMC) code developed by the Nuclear Research and Consultancy Group (NRG) (Rochman et al., 2014). ...
... See (Bostelmann, 2020) for details on standard and conditional sampling. ...
... This work focuses on the demonstration of R 2 and SPC 2 as implemented in the SCALE's Sampler sequence. The calculation of Sobol' main effect and total effect sensitivity indices was previously demonstrated and shown to provide almost consistent results with R 2 and SPC 2 (Bostelmann, 2020). The same study also developed and demonstrated corresponding indices that are calculated using sensitivity coefficients from perturbation theory. ...
Nuclear data are a major source of uncertainties in reactor physics calculations. The propagation of nuclear data uncertainties to important system responses is instrumental when determining appropriate safety margins in reactor safety analyses. It is also important to understand the major contributors to the observed uncertainties to make recommendations for further measurements and evaluations and aid in the understanding of the studied system.
The SCALE code system allows for nuclear data uncertainty analysis based on the random sampling approach as implemented in SCALE’s Sampler sequence. Sampler was recently extended by a sensitivity analysis in terms of the calculation of two correlation-based sensitivity indices. This analysis allows for the identification of the top contributing nuclear reactions to any analyzed output uncertainty. This paper presents the sensitivity indices, along with their interpretation and limitations. It demonstrates the application in an eigenvalue and decay heat analysis for a boiling water reactor fuel assembly.
... The major contributor to the uncertainty of many reactivity coefficients in these systems is 238 U inelastic scattering due to its large uncertainty in the fast energy range. Other relevant contributors to reactivity coefficients uncertainties, are the scattering reactions of 23 Na as the coolant and 56 Fe as the major component in structural materials [8]. ...
... Testing and validation for application to non-LWR systems is ongoing. Recent activities with respect to SCALE's SFR applications include nuclear data performance assessments for fast-spectrum systems [8][9][10]13] and cross section processing development [14]. Current modeling efforts concern several non-LWR systems for the validation of SCALE and the support of several application activities, including severe accident analysis and nuclear data performance assessment. ...
... Since TSUNAMI does not permit the direct calculation of sensitivity coefficients for power, the random sampling approach as implemented in SCALE's Sampler sequence [21] was used to study uncertainties resulting from nuclear data of the radial power profile. To identify the top contributing nuclide reactions to the output uncertainty, Sampler calculates the sensitivity index R 2 [8] of all reactions of all nuclides relevant for the model. On a level from 0 to 1, R 2 provides a measure of the importance of an individual nuclear reaction to the observed output uncertainty. ...
The EBR-II benchmark, which was recently included in the International Handbook of Evaluated Reactor Physics Benchmark Experiments, served as a basis for assessing the performance of the SCALE code system for fast reactor analyses. A reference SCALE model was developed based on the benchmark specifications. Great agreement was observed between the eigenvalue calculated with this SCALE model and the benchmark eigenvalue. To identify potential gaps and uncertainties of nuclear data for the simulation of various quantities of interest in fast spectrum systems, sensitivity and uncertainty analyses were performed for the eigenvalue, reactivity effects, and the radial power profile of EBR-II using the two most recent ENDF/B nuclear data library releases. While the nominal results are consistent between the calculations with the different libraries, the uncertainties due to nuclear data vary significantly. The major driver of observed uncertainties is the uncertainty of the 235U (n,γ) reaction. Since the uncertainty of this reaction is significantly reduced in the ENDF/B-VIII.0 library compared to ENDF/B-VII.1, the obtained output uncertainties tend to be smaller in ENDF/B-VIII.0 calculations, although the decrease is partially compensated by increased uncertainties in 235U fission and ν¯.
... These perturbed nuclear data libraries are then used to perform the reactor physics calculation of interest-one calculation for each perturbed dataset. A statistical analysis of the multiple outputs provides the uncertainties in the output quantity of interest, and the analysis also identifies important nuclide reactions by means of correlation coefficients (Williams et al. 2013, Bostelmann 2020. ...
... The review of uncertainty analysis studies using sensitivity coefficients for SFRs revealed a large significance of scattering reactions of the coolant (Na) and structural materials ( 56 Fe, in particular) (OECD/NEA 2016, Bostelmann et al. 2018a, Bostelmann 2020. Furthermore, for fast spectrum systems, the (n,2n) reaction has a greater importance than in LWR systems (Yang 2012). ...
... Furthermore, for fast spectrum systems, the (n,2n) reaction has a greater importance than in LWR systems (Yang 2012). In case of oxide fuel, elastic scattering of 16 O is relevant because of its resonances in the fast energy range (Bostelmann et al. 2018a, Bostelmann 2020. ...
Advanced reactor concepts currently being developed throughout the industry are significantly different from light water reactor (LWR) designs with respect to geometry, materials, and operating conditions, and consequently, with respect to their reactor physics behavior. Given the limited operating experience with non-LWRs, the accurate simulation of reactor physics and the quantification of associated uncertainties are critical for ensuring that advanced reactor concepts operate within the appropriate safety margins. Nuclear data are a major source of input uncertainties in reactor physics analysis. As part of an ongoing project at Oak Ridge National Laboratory (ORNL), the effects of nuclear data uncertainties on key figures of merit associated with advanced reactor safety are being assessed for selected advanced reactor technologies. Key nuclear data relevant for reactor safety analysis for each selected advanced reactor technology were identified, and their impact on important key figures of merit was assessed. Available advanced reactor specifications were reviewed, results from studies performed at ORNL and other research institutions were consulted, and available evaluated nuclear data libraries were analyzed. This report summarizes the key nuclear data for nuclides in the fuel, as well as other significant data, including scattering and neutron capture in various materials for the moderator, coolant, and structure of the considered advanced reactors. For the considered advanced reactors that use low-enriched uranium (LEU) fuel, results from LWR studies provided insight into relevant nuclear data given the lack of available studies specifically addressing these new systems. The major nominal missing data that were identified consist of thermal scattering data and 135mXe cross section data for molten salt reactor (MSR) analysis. The identified major gaps with respect to nuclear data uncertainties are missing uncertainties of thermal scattering data for high temperature gas-cooled reactors and moderated MSR systems, and incomplete uncertainties on angular distributions in particular for fast spectrum systems, such as sodiumcooled fast reactors, fast molten salt reactors, and heat pipe reactors. Furthermore, it was found that special attention should be paid to cross section and uncertainty differences between different evaluated nuclear data library releases, because significant differences in nuclear data that can lead to major differences in reactivity calculations were found, even for well-known nuclides.
... A 1% perturbation in 235 U( ) / 235 U( ) is therefore almost 2.5 standard deviations of the , , compared to 1/40 th of the 239 Pu(n,γ) / 239 Pu(n,γ) , standard deviation. Bostelmann (2020) provides an in-depth comparison of three sensitivity methods in her U/SA of SFR systems, and concluded that the correlation-based sensitivity indices (e.g. R 2 or SPC 2 ) provided very similar results with much less effort required to calculate variance-based indices such as Sobol's main sensitivity index (Sobol, 2001). ...
... The development of a rigorous sensitivity assessment statistical methodology applied to HTGRs could be an area of possible future research. An example of such a recent scheme developed for SFR designs can be found in the work of Bostelmann (2020). Up to now, current attempts at developing sensitivity assessment capabilities have been exclusively focused on neutronics stand-alone cases. ...
... A notable improvement on the current approach will therefore be the implementation of variance-based sensitivity indicators like Sobol's first order and total indices (Sobol, 2001), or rather variance-based indices based on linear perturbation theory, as suggested by Bostelmann (2020 ...
As one of the Generation-IV advanced reactor types, High Temperature Gas-Cooled Reactors (HTGRs) can provide high-quality heat to industrial processes, in addition to saleable and inherently safe power operation. In the United States, several small- and micro-HTGR projects are currently underway, and the assessment of uncertainties in the modelling and simulation of HTGRs is an important aspect of the design and licensing process.
The research reported in this dissertation is focussed on providing a practical example of a statistical uncertainty and sensitivity assessment (U/SA) methodology that can be used by HTGR designers, national nuclear regulators and academic institutions to assess the impact of input uncertainties, across many scales, multiple physics, and time, for several important Figures of Merit (FOMs) such as the core eigenvalue, peak spatial power and maximum fuel temperature. In addition to the quantification of uncertainty in these output parameters, the sensitivity assessment identifies the main contributors to the uncertainties and provides a rationale for future improvements in nuclear data, material property and operational condition uncertainties.
The main objective of this work is the development of a consistent U/SA that can be applied from the lattice to the core spatial domain, and propagation of the non-linear coupled uncertainties that exists between reactor physics and thermal fluid phenomena. The selection of the statistical U/SA approach is motivated by several critical factors unique to HTGRs; the most important being the lack of experimental or operational validation databases and the presence of non-linear phenomena (e.g. coolant bypass flows, graphite thermal conductivity change with irradiation exposure).
The scope of this work includes an assessment of uncertainties in cross-sections, operational boundary conditions and thermal fluid parameters. Two novel contributions include the impact of uncertainties in the core bypass flows on the maximum fuel temperature, and comparisons of the uncertainty and sensitivity results obtained utilizing three energy group structures (2-, 8- and 26 groups).
The proposed methodology is applied to the U/SA of the prismatic modular high-temperature gas-cooled reactor (MHTGR)-350 design, and specifically within the context of the International Atomic Energy Agency (IAEA) Coordinated Research Program (CRP) on HTGR Uncertainty in Modelling (UAM). One of the main contributions of this research is the development of the HTGR UAM benchmark specifications that covers the simulation domain in a phased-approach from the generation of block-level cross-sections to the coupled neutronic/thermal fluid analysis of two important safety case transients (the Control Rod Withdrawal and Pressurised Loss of Cooling events).
The statistical U/SA methodology is successfully implemented and demonstrated using the INL-developed codes PHISICS, RELAP5-3D and RAVEN for the stand-alone and coupled core steady-states and transients, based on perturbed cross-section libraries obtained from the SCALE/Sampler sequence.
Uncertainties in nuclear data (cross-sections and the average number of neutrons produced per fission, 235U[𝑣 ]) lead to standard deviations (uncertainties of one σ) of approximately 0.5% in the core eigenvalues of various fresh and mixed MHTGR-350 lattice and core models. For the coupled neutronics/thermal fluid model, local power density uncertainties up to 3.6% were observed in the colder regions of the core, while the local maximum fuel temperature uncertainties reached 1.5% for the models that included thermal fluid uncertainties. The addition of thermal fluid uncertainties dominated the impacts of nuclear data uncertainties in all cases, and it was successfully demonstrated that the statistical methodology propagates the uncertainties from the lattice models to the coupled transients in a consistent manner.
The main contributors to uncertainties in the power density and fuel temperatures during the two transients were uncertainties in the reactor operating conditions (total power, inlet mass flow rate and inlet gas temperature). Variations in the bypass flows did not have significant impact on any of the output variables. For the nuclear data uncertainties it was found that the 235U(𝑣 ) / 235U(𝑣 ) covariance produced the largest sensitivities in terms of its impact on the eigenvalue and peak reactor power. It was also observed that the impact of any nuclear data uncertainties on the maximum fuel temperature was much less significant that the impact on eigenvalue and power.
Another important finding was that although the use of eight or more energy groups is recommended for best-estimate HTGR simulation, two-group models produced acceptable uncertainty and sensitivity results for most FOMs. Since the statistical U/SA methodology is computationally expensive, and most transient solver requirements will scale directly with the number of energy groups, two energy groups could be used by HTGR developers during the early stages of design when larger uncertainty margins can be tolerated.
