Serpent/SCF pin-level multiphysics solutions for the VERA Fuel Assembly benchmark
Introduction
The continuous improvement in nuclear industry safety standards and reactor designers’ and operators’ commercial goals provides a driving force to the development of highly accurate methodologies in reactor physics. The global trend is usually oriented to improve the prediction capabilities of specific reactor’s parameters under steady state and transient scenarios by the use of coupled state-of-the-art calculation codes. During the past years an important effort was observed worldwide in collaborative projects aimed to develop high accurate multiphysics approaches for nuclear reactor analysis (CASL, 2010, Gaston et al., 2015, HPMC, 2011).
Under this framework, the European Research and Innovation project McSAFE (NUGENIA association, 2017, Luigi Mercatali et al., 2017) is a coordinated effort held by 12 institutions from 7 different countries around the EU and an extended community of users around the world that aims to tackle this demand. This McSAFE project represents a continuation of past efforts (HPMC, 2011, Ivanov et al., 2013, Ivanov et al., 2015), developed as proof of concept of main challenges. As a result, this project, which has started in September 2017, has the main objective of moving Monte Carlo (MC) stand-alone and coupled solution methodologies to become valuable tools for industry like applications for LWRs of generations II and III. As part of this project several developments in coupling strategies for transient and steady-state calculations are being developed, implemented and tested.
Specific MC code goals under McSAFE include full core LWR calculations, both including depletion and Thermal Hydraulic (TH) feedback in a full core approach. Moving towards these high-fidelity calculation approaches states a challenge not only from the multi-physics point of view, but also from several aspects related to computational requirements and massive parallelization (Ivanov et al., 2013, Ferraro et al., 2018). In addition, the statistical behaviour of MC codes also play a key role both regarding convergence aspects and statistical noise amplification.
To tackle those issues, the capabilities assessment together with the imperative verification and validation process are carried out inside McSAFE in a graded approach by the detailed verification with high-quality numerical benchmarks in a first stage, together with a foreseen comparison with experimental data in a second stage. Consequently, the present work develops the coupled Neutronics-TH Fuel Assembly problem stated in the VERA Benchmark (namely VERA problem #6 (Godfrey, 2014)) proposed by the CASL consortium (CASL, 2010) using the available tools and methodology.
For this purpose a pin-by-pin coupling scheme using the Serpent 2 MC code (developed by VTT, Finland (Leppänen et al., 2013)) and the subchannel code SUBCHANFLOW (referred here also as SCF, developed by KIT, Germany (Imke et al., 2012)) was developed, together with the analysis of main convergence issues.
The MC plus subchannel TH coupling approach was already been proposed in previous developments (Daeubler et al., 2015) in a master-slave approach, which encouraged to develop a detailed analysis for a high fidelity benchmark, as proposed in the present work.
For this present work, an external coupling is proposed to solve a high-fidelity benchmark based in Multi-physics Files (as developed in Valtavirta (2017) and is described in Serpent developer team (2018)). This decision was held in this case due to the stated workpath is oriented to develop the main criteria and strategies for the following coupling strategies to be implemented, namely externally supervised API approach, which departs from the traditional master-slave approach developed in former works (Daeubler et al., 2015). In addition, this decision allows to easily test and implement diverse concepts such as convergence criteria, relaxations schemes and temperature averaging schemes.
As a result, this work proposes the VERA problem #6 solution, where both global parameters (such as reactivity, average power profiles, integrated pin power distributions and outlet coolant temperatures) and local parameters (such as axial power profiles and axial coolant temperatures for specific rods and channels respectively) are analyzed.
It should be regarded that despite no reference results are provided in benchmark specifications (Godfrey, 2014) for Problem #6, other high-fidelity projects provide reported values in open publications (Aviles et al., 2017, Kochunas et al., 2014, Wilderman et al., 2015), which are used in this work to verify main results obtained. It is important to note here that the scope of this work is not aimed to reproduce a specific results from a third party project, but to present the main aspects and insights of the proposed approach.
In addition, other key aspects regarding convergence criteria are also to be analyzed in order to assess the global behaviour of the coupled problem and to provide the basis for more complex problems analysis to be further developed. The main issue to consider in this point is the fact that the statistical nature of MC codes leads to a potential amplification of statistical noise, which has to be analyzed in advance (Valtavirta, 2017). Furthermore, as far as the average running time of MC codes is several orders of magnitude higher than those from TH subchannel codes, a wise choice of relaxation schemes between iterations is compulsory.
Dealing with this combined problem represents a challenging issue, where obtaining a general solution usually requires the application of highly-advanced techniques (Aufiero and Fratoni, 2017) outside of the scope of this work. For such reason, an holistic approach is proposed, which consists of a three steps procedure:
- 1.
Estimate the propagation of MC power error in the coupled convergence criteria.
- 2.
Adjust the MC convergence and coupling convergence criteria based on step 1.
- 3.
Test the convergence using step 2 together with a relaxation of TH fields.
Using this approach, results were obtained without dealing with unrealistic convergence criteria and also avoiding unstable behaviour of the coupled solution iteration. In addition the insights gained are valuable for the coupling approaches and criteria to be further developed under McSAFE project.
Finally, the impact of different fuel temperature averages when mapping TH fields is also briefly discussed. This additional study is deemed to provide a raw estimation of the effect in main calculated parameters, within the scope of a high-fidelity goals.
Section snippets
VERA problem #6
The VERA benchmark consists of a series of calculations for a standard Westinghouse 17x17 PWR design (Godfrey, 2014), that provides a gradual approach from pin level to full core with TH feedback and burnup. In this benchmark diverse FA configurations are analyzed in terms of burnable poisons, control rods (CR) configurations and TH parameters. Nevertheless, for the scope of this work, only problem #6 is analyzed (Godfrey, 2014). This case represents a BOC (fresh) fuel assembly 3D case, to be
Modeling approach
The modeling approach relies heavily in the extensive use of advanced features available in the MC code Serpent (Leppänen et al., 2013, Valtavirta, 2017) together with specific features of SUBCHANFLOW code which can be summarized as:
- •
The capability of Serpent to handle Multiphysics Interface Files (IFC) (Valtavirta, 2017), that allows to superimpose over a given 3D geometry TH fields, such as temperatures or densities for diverse materials.
- •
The capability available in Serpent to handle variable
Results
This section presents the main obtained results for the VERA problem #6, including global parameters (such as reactivity, average power profiles, integrated pin power distributions and outlet coolant temperatures) and local parameters (such as axial power profiles and axial coolant temperatures for specific rods and channels respectively). These results were obtained considering 3000 active cycles of 1E + 05 histories each (i.e. 3E + 08 active histories in total), including a conservative 50
Main results discussion
From the in-depth analysis of the results presented in Section 4 it should be regarded that:
- a.
A good coupled convergence behaviour is observed. In addition, the practical approach to preliminary quantify the convergence criteria was shown to be effective.
- b.
A good agreement was found in the comparison with reported results from other high-fidelity, not only regarding global paramaters comparisons, but also for detailed axial profiles such as power by pin of coolant TH fields at subchannel level.
- c.
The
Further work
The results obtained in previous sections, both related to the global agreement of integral and detailed calculation results together with the good convergence behaviour, encourages to continue to further steps of high fidelity modelling. As a result, to finally tackle the project goals the next steps would include several aspects such as:
- a.
Scalability analysis on High Performance Computer (HPC) environments: The scalability of the problem in massive parallel architectures is to be investigated.
Conclusions
The assessment of capabilities together with the imperative verification and validation process for the methodologies and schemes proposed play a key role under McSAFE high -fidelity project. The in-depth analysis of the Fuel Assembly coupled Neutronic-TH VERA Benchmark problem #6 proposed by CASL consortium (Godfrey, 2014) represents a perfect testing case, both regarding the results verification and the problem convergence aspects analysis. The scheme presented in this work, using the
Conflict of interest
The authors declare no conflict of interest.
Acknowledgments
This work was done within the McSAFE project which is receiving funding from the Euratom research and training programme 2014–2018 under grant agreement No 755097.
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2022, Annals of Nuclear EnergyCitation Excerpt :Conversely, the differences in the PPF can directly affect the pin-power reconstruction, thus an accurate representation is expected. For this case, the use of diverse codes, NDL and models can lead to differences in the order of half percents, but with values up to 1–2 [%] if strong absorbers are included (Ferraro et al., 2019; Kim, 2018; Nguyen et al., 2020; Choi, 2017), specially if Gd pins are considered. This Section presents the main results obtained with Condor, including the comparisons with the reference values and the Serpent models.
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2020, Nuclear Engineering and DesignCitation Excerpt :These all are heavily interdependent of each other, and thus, computer codes applied for reactor design, operation and safety analyses aiming to accurately predict the behaviour of a reactor need to account for the relevant feedbacks between the various processes. Although such computer codes have already been developed and used for decades, the evolution of computer hardware makes it feasible to utilise computationally expensive calculation approaches based on less approximations and more on first principles for best-estimate analyses at an increasingly larger scale and for more industry-like applications (Ferraro et al., 2019), even considering couplings between the multiple physics. Development and improvement of such analysis capabilities is constantly ongoing in several projects ranging from large efforts that can involve multiple countries or organisations, such as the development of the European NURESIM platform (Chauliac et al., 2011), the MOOSE simulation environment at the Idaho National Laboratory (Gaston et al., 2009) or the work within the CASL consortium established by the US Department of Energy (Turinsky and Kothe, 2016), to more modest, yet still very useful contributions by individual organisations or research groups.
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2020, Annals of Nuclear EnergyCitation Excerpt :Several coupling implementation schemes for such codes have been developed for steady-state and transient problems, both for square and hexagonal geometries. These include the standard external coupling (Faucher, 2019; Ferraro et al., 2019a), an object oriented internal coupling (García et al., 2019) and an internal master-slave (namely embedded) coupling. In this work, the embedded master-slave coupling approach is considered, referred here as master-slave.