Application case for phase III of UAM-LWR benchmark: Uncertainty propagation of thermal-hydraulic macroscopic parameters

[EN] This work covers an important point of the benchmark released by the expert group on Uncertainty Analysis in Modeling of Light Water Reactors. This ambitious benchmark aims to determine the uncertainty in light water reactors systems and processes in all stages of calculation, with emphasis on multi-physics (coupled) and multi-scale simulations. The Gesellschaft für Anlagen und Reaktorsicherheit methodology is used to propagate the thermal-hydraulic uncertainty of macroscopic parameters through TRACE5.0p3/PARCSv3.0 coupled code. The main innovative points achieved in this work are i) a new thermal-hydraulic model is developed with a highly-accurate 3D core discretization plus an iterative process is presented to adjust the 3D bypass flow, ii) a control rod insertion occurrence ¿which data is obtained from a real PWR test¿ is used as a transient simulation, iii) two approaches are used for the propagation process: maximum response where the uncertainty and sensitivity analysis is performed for the maximum absolute response and index dependent where the uncertainty and sensitivity analysis is performed at each time step, and iv) RESTING MATLAB code is developed to automate the model generation process and, then, propagate the thermal-hydraulic uncertainty. The input uncertainty information is found in related literature or, if not found, defined based on expert judgment. This paper, first, presents the Gesellschaft für Anlagen und Reaktorsicherheit methodology to propagate the uncertainty in thermal-hydraulic macroscopic parameters and, then, shows the results when the methodology is applied to a PWR reactor.The authors of this work thank the UAM-LWR benchmark organizers without whom this work would not have been possible. Besides, the authors sincerely thank to the Ministerio de Economia, Industria y Competitividad and the "Plan Nacional de I+D+i" for funding the projects NUC-MULTPHYS ENE2012-34585 and ENE2017-89029-P.Mesado, C.; Miró Herrero, R.; Verdú Martín, GJ. (2020). Application case for phase III of UAM-LWR benchmark: Uncertainty propagation of thermal-hydraulic macroscopic parameters. Nuclear Engineering and Technology. 52(8):1626-1637. https://doi.org/10.1016/j.net.2020.01.010S1626163752

Cross-Section Generation Using TXT2NTAB Code for Uncertainty Propagation with Burnup Dependence

[EN] One of the challenges of studying the neutronics of reactors is to generate reliable parameterized libraries that contain information to simulate the core in all possible operational and transient conditions. These libraries must include tables of cross sections and other neutronic and kinetic parameters and are obtained by simulating all the segments in a transport code. At the lattice level, one can use branch calculations to change ¿instantaneously¿ the feedback parameters as a function of burnup. When using random sampling for the lattice calculations, one can obtain statistical information about the output parameters and use it in a core simulation to characterize the accuracy of data estimating uncertainties when simulating a heterogeneous system at different scales of detail. This work presents the methodology to generate NEMTAB libraries from data obtained in the SCALE code system to be used in PARCS simulations. The code TXT2NTAB is used to reorder the cross-section tables in NEMTAB format and generate another NEMTAB of standard deviation. With these libraries, the authors perform a steady-state calculation for a light water reactor to propagate several uncertainties at the core level. The methodology allows obtaining statistical information of the most important output parameters: multiplication factor keff, axial power peak Pz, and axial peak node Nz.This work has been partially supported by Spanish Ministerio de Economia y Competitividad under projects ENE2017-89029-P.Labarile, A.; Mesado, C.; Miró Herrero, R.; Verdú Martín, GJ. (2019). Cross-Section Generation Using TXT2NTAB Code for Uncertainty Propagation with Burnup Dependence. Nuclear Technology. 205(12):1675-1684. https://doi.org/10.1080/00295450.2019.16310511675168420512D’Auria, F., Camargo, C., & Mazzantini, O. (2012). The Best Estimate Plus Uncertainty (BEPU) approach in licensing of current nuclear reactors. Nuclear Engineering and Design, 248, 317-328. doi:10.1016/j.nucengdes.2012.04.002K. IVANOV et al. “Benchmarks for Uncertainty Analysis in Modelling (UAM) for Design, Operation and Safety Analysis of LWRs,” NEA/NSC/DOC(2009)11, Organisation for Economic Co-Operation and Development, Nuclear Energy Agency (2016).Wilks, S. S. (1941). Determination of Sample Sizes for Setting Tolerance Limits. The Annals of Mathematical Statistics, 12(1), 91-96. doi:10.1214/aoms/1177731788“SCALE: A Comprehensive Modelling and Simulation Suite for Nuclear Safety Analysis and Design,” ORNL/TM-2005/39, Version 6.1, Oak Ridge National Laboratory (2011).S. GOLUOGLU et al. “The Material Information Processor for SCALE,” Technical Report, Oak Ridge National Laboratory (2011).Gauld, I. C., Radulescu, G., Ilas, G., Murphy, B. D., Williams, M. L., & Wiarda, D. (2011). Isotopic Depletion and Decay Methods and Analysis Capabilities in SCALE. Nuclear Technology, 174(2), 169-195. doi:10.13182/nt11-3DeHart, M. D., & Bowman, S. M. (2011). Reactor Physics Methods and Analysis Capabilities in SCALE. Nuclear Technology, 174(2), 196-213. doi:10.13182/nt174-196Williams, M. L., Ilas, G., Jessee, M. A., Rearden, B. T., Wiarda, D., Zwermann, W., … Pautz, A. (2013). A Statistical Sampling Method for Uncertainty Analysis with SCALE and XSUSA. Nuclear Technology, 183(3), 515-526. doi:10.13182/nt12-112“DAKOTA Statistical Tool”; http://www.cs.sandia.gov/DAKOTA/ (current as of Jan. 28, 2019).T. DOWNAR et al. “PARCS V3.0 U.S. NRC Core Neutronics Simulator User Manual,” Technical Report, Department of Nuclear Engineering and Radiological Sciences. University of Michigan (2012).G. STRYDOM et al. “IAEA CRP on HTGR UAM: Propagation of Phase I Cross Section Uncertainties to Phase II Neutronics Steady State Using SCALE/SAMPLER and PHISICS/RELAP5-3D”; https://www.osti.gov/servlets/purl/1478196 (current as of Jan. 28, 2019).B. J. ADE, “SCALE/TRITON Primer: A Primer for Light Water Reactor Lattice Physics Calculations,” NUREG/CR-7041, Oak Ridge National Laboratory (2012).Ilas, G., Gauld, I. C., & Radulescu, G. (2012). Validation of new depletion capabilities and ENDF/B-VII data libraries in SCALE. Annals of Nuclear Energy, 46, 43-55. doi:10.1016/j.anucene.2012.03.01

Calculation of multiple eigenvalues of the neutron diffusion equation discretized with a parallelized finite volume method

[EN] The spatial distribution of the neutron flux within the core of nuclear reactors is a key factor in nuclear safety. The easiest and fastest way to determine it is by solving the eigenvalue problem of the neutron diffusion equation, which only contains spatial derivatives. The approximation of these derivatives is performed by discretizing the geometry and using numerical methods. In this work, the authors used a finite volume method based on a polynomial expansion of the neutron flux. Once these terms are discretized, a set of matrix equations is obtained, which constitutes the eigenvalue problem. A very effective class of methods for the solution of eigenvalue problems are those based on projection onto a low-dimensional subspace, such as Krylov subspaces. Thus, the SLEPc library was used for solving the eigenvalue problem by means of the Krylov-Schur method, which also uses projection methods of PETSc for solving linear systems. This work includes a complete sensitivity analysis of different issues: mesh, polynomial terms, linear systems solvers and parallelization.This work has been partially supported by the Spanish Ministerio de Eduacion Cultura y Deporte under the grant FPU13/01009, the Spanish Ministerio de Ciencia e Innovacion under the project ENE2014-59442-P, the Spanish Ministerio de Economia y Competitividad and the European Fondo Europeo de Desarrollo Regional (FEDER) under the project ENE2015-68353-P (MINECO/FEDER), the Generalitat Valenciana under the project PROMETEOII/2014/008, and the Spanish Ministerio de Economia y Competitividad and the European Fondo Europeo de Desarrollo Regional (FEDER) under the project TIN2016-075985-P.Bernal-Garcia, A.; Roman, JE.; Miró Herrero, R.; Verdú Martín, GJ. (2018). Calculation of multiple eigenvalues of the neutron diffusion equation discretized with a parallelized finite volume method. Progress in Nuclear Energy. 105:271-278. https://doi.org/10.1016/j.pnucene.2018.02.006S27127810

Development and validation of a one-dimensional solver in a CFD platform for boiling flows in bubbly regimes

[EN] This paper presents a new one-dimensional solver for two-phase flow simulations where boiling is involved. The solver has been implemented within the OpenFOAM® platform. The basic formulation follows the Eulerian description of the Navier¿Stokes equations. Different closure equations for one-dimensional simulations are also included, as well as a subcooled boiling model in order to perform accurate computations of the mass and heat transfer between phases. In addition to the fluid, a domain is included in order to represent the solid structure, so the solver is able to solve conjugate heat transfer problems. Two different test cases are presented in this work, first a single-phase test case in order to verify the conjugate heat transfer, and then a case based on the Bartolomej international benchmark, which consists of a vertical pipe where the fluid runs upwards while it is heated. Transient calculation were performed, and the results were compared to the TRACE system code, and to the experimental data in the corresponding case. With this calculations, the capability of this new solver to simulate one-dimensional single-phase and two-phase flows including boiling is demonstrated. This work is a first step of a final objective, which consists in allowing a 1D¿3D coupling within the CFD platform, avoiding external links.This work has been partially supported by the Spanish Agencia Estatal de Investigacion [grant number BES-2013-064783], and the Spanish Ministerio de Economia Industria y Competitividad [project NUC-MULTPHYS ENE2012-34585].Gomez-Zarzuela-Quel, C.; Chiva Vicent, S.; Peña-Monferrer, C.; Miró Herrero, R. (2021). Development and validation of a one-dimensional solver in a CFD platform for boiling flows in bubbly regimes. Progress in Nuclear Energy. 134:1-16. https://doi.org/10.1016/j.pnucene.2021.103680S11613

Multigroup neutron diffusion equation with the finite volume method in reactors using MOX fuels

[EN] The use of mixed oxide (MOX) fuel to partially fill the cores of commercial light water reactors (LWRs) gives rise to a reduction of the radioactive waste and production of more energy. However, the use of MOX fuels in LWRs changes the physics characteristics of the reactor core, since the variation with energy of the cross sections for the plutonium isotopes is more complex than for the uranium isotopes. Although the neutron diffusion theory could be applied to reactors using MOX fuels, more emphasis on treatment of the energy discretization should be placed. This energy discretization could be typically 4¿8 energy groups, instead of the standard 2-energy group approach. In this work, the authors developed a finite volume method for discretizing the general multigroup neutron diffusion equation. This method solves the eigenvalue problem by using Krylov projection methods, in which the size of the vectors used for building the Krylov subspace does not depend on the number of energy groups, but it can solve the multigroup formulation with upscattering and fission production terms in several energy groups. The method was applied to MOX reactors for its validation. © 2017 Atomic Energy Society of Japan. All rights reserved.This work has been partially supported by the Spanish Ministerio de Eduacion Cultura y Deporte [grant number FPU13/01009]; the Spanish Ministerio de Ciencia e Innovacion [project ENE2014-59442-P]; the Spanish Ministerio de Economia y Competitividad and the European Fondo Europeo de Desarrollo Regional (MINECO/FEDER) [project ENE2015-68353-P]; the Generalitat Valenciana [project PROMETEOII/2014/008]; and the Spanish Ministerio de Economia y Competitividad [project TIN2016-75985-P].Bernal-Garcia, A.; Roman, JE.; Miró Herrero, R.; Verdú Martín, GJ. (2017). Multigroup neutron diffusion equation with the finite volume method in reactors using MOX fuels. Journal of Nuclear Science and Technology. 54(11):1251-1260. https://doi.org/10.1080/00223131.2017.1359120S12511260541

Development of a 3D deterministic fuel depletion code

[EN] Predicting the isotopic evolution and its impact in the core performance becomes crucial for designing and operating nuclear reactors. This work faces the starting point of developing a depletion code using the latest advances in numerical computing. MATLAB will be used to create a depletion program, getting the necessary nuclear data from the SCALE code system. Burn-up chains, managing of the proper nuclear data, creating, and solving ODE systems are analysed in the present work. As a result, a fuel depletion code was created. The code can perform depletion calculations for a single fuel material for a reduced burn-up chain. The relative error between the obtained and the reference nuclides concentrations is considerably low. The general assumptions, requirements and methodology for creating a depletion code have been analysed and verified.This work has been partially supported by the Spanish Agencia Estatal de Investigación [grant number PRE2019-089431], [project PGC2018-096437-B-I00-AR].Vivancos-Grau, A.; Barrachina, T.; Miró Herrero, R.; Verdú Martín, GJ.; Bernal, A. (2021). Development of a 3D deterministic fuel depletion code. European Nuclear Society. 1-10. http://hdl.handle.net/10251/19108111

PARCS vs CORE SIM neutron noise simulations

[EN] In a nuclear reactor, even operating at full power and steady-state conditions, fluctuations are detected in the recording of any process parameter. These fluctuations (also called noise) could be of various origins, such as, turbulence, mechanical vibrations, coolant boiling, etc. The monitoring and complete comprehension of those parameters should thus allow detecting, using existing instrumentation and without introducing any external perturbation to the system, possible anomalies before they have any inadvertent effect on plant safety and availability. In order to reproduce and study the induced neutron noise in a nuclear reactor core, it is compulsory to develop suitable tools. Existing time-domain codes were originally not developed for this type of calculations. Modifications of those codes and the development of an associated intricate methodology are necessary for enabling noise calculations. This involves, in some cases, changes in the source code and the development of new auxiliary tools to ensure accurate reproductions of the core behavior under the existence of a neutron noise source. In the proposed work, the time-domain neutron diffusion code PARCS is used to model the effect of stationary perturbations representative of given neutron noise sources. In order to validate the feasibility of the time-dependent methodology thus developed, comparisons with the results of simulations performed in the frequency domain, using the CORE SIM tool, developed at Chalmers University of Technology, are performed. The development of a few test cases based on a real reactor model are undertaken as the basis for such comparisons and a methodology aimed at assessing the time-domain simulations versus the frequency-domain simulations is established. It is demonstrated that PARCS, although not primarily developed for neutron noise calculations, can reproduce neutron noise patterns for reasonable frequencies. However, it is also observed that unphysical results are occasionally obtained.This work was carried out under the pre-doctoral contract FPI Subprogram 1 and mobility aids of the Universitat Politècnica de València and the support of the Spanish Ministerio de Ciencia e Innovación under the project ENE2017-89029-P. The research leading to these results was also partially funded from the Euratom research and training programme 2014 2018 under grant agreement No 754316 (CORTEX project).Olmo-Juan, N.; Demazière, C.; Barrachina, T.; Miró Herrero, R.; Verdú Martín, GJ. (2019). PARCS vs CORE SIM neutron noise simulations. Progress in Nuclear Energy. 115:169-180. https://doi.org/10.1016/j.pnucene.2019.03.041S16918011

Assembly Discontinuity Factors for the Neutron Diffusion Equation discretized with the Finite Volume Method. Application to BWR

This is the author’s version of a work that was accepted for publication in Annals of Nuclear Energy. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Annals of Nuclear Energy, vol. 97 (2016) DOI 10.1016/j.anucene.2016.06.023.The neutron flux spatial distribution in Boiling Water Reactors (BWRs) can be calculated by means of the Neutron Diffusion Equation (NDE), which is a space- and time-dependent differential equation. In steady state conditions, the time derivative terms are zero and this equation is rewritten as an eigenvalue problem. In addition, the spatial partial derivatives terms are transformed into algebraic terms by discretizing the geometry and using numerical methods. As regards the geometrical discretization, BWRs are complex systems containing different components of different geometries and materials, but they are usually modelled as parallelepiped nodes each one containing only one homogenized material to simplify the solution of the NDE. There are several techniques to correct the homogenization in the node, but the most commonly used in BWRs is that based on Assembly Discontinuity Factors (ADFs). As regards numerical methods, the Finite Volume Method (FVM) is feasible and suitable to be applied to the NDE. In this paper, a FVM based on a polynomial expansion method has been used to obtain the matrices of the eigenvalue problem, assuring the accomplishment of the ADFs for a BWR This eigenvalue problem has been solved by means of the SLEPc library. (C) 2016 Elsevier Ltd. All rights reserved.This work has been partially supported by the Spanish Ministerio de Eduacion Cultura y Deporte under the grant FPU13/01009, the Spanish Ministerio de Ciencia e Innovacion under projects ENE2014-59442-P, the Spanish Ministerio de Economia y Competitividad and the European Fondo Europeo de Desarrollo Regional (FEDER) under project ENE2015-68353-P (MINECO/FEDER), the Generalitat Valenciana under projects PROMETEOII/2014/008, the Universitat Politecnica de Valencia under project UPPTE/2012/118, and the Spanish Ministerio de Economia y Competitividad under the project TIN2013-41049-P.Bernal-Garcia, A.; Román Moltó, JE.; Miró Herrero, R.; Verdú Martín, GJ. (2016). Assembly Discontinuity Factors for the Neutron Diffusion Equation discretized with the Finite Volume Method. Application to BWR. Annals of Nuclear Energy. 97:76-85. https://doi.org/10.1016/j.anucene.2016.06.023S76859

Desarrollo de un código neutrónico de difusión 2D y 3D estacionario por el Método de Volúmenes Finitos

El objetivo del trabajo es el desarrollo de un código neutrónico modal de difusión en 2D y 3D estacionario utilizando el Método de Volúmenes Finitos, a partir de códigos libres y que se pueda aplicar a reactores de cualquier geometría. Actualmente, los métodos numéricos que más se utilizan en lo códigos de difusión proporcionan buenos resultados en malla estructurada, pero su aplicación a malla no estructurada no es fácil y puede presentar problemas de convergencia y estabilidad de la solución. Respecto a la malla no estructurada, su uso está justificado por su fácil adaptación a geometrías complejas y por el desarrollo de códigos acoplados termohidráuliconeutrónico, así como el desarrollo de códigos fluidodinámicos (CFD) que incentivan el desarrollo de un código neutrónico que tenga la misma malla que la de los códigos fluidodinámicos, que en general suele ser no estructurada. Por otra parte, el refinamiento de la malla y su adaptación a geometrías complejas es otro estímulo de cara a conocer con más detalle lo que ocurre en el núcleo del reactor. Finalmente, el código se ha validado con la simulación de un reactor homogéneo y otro heterogéneo para 2D y 3DBernal García, Á.; Miró Herrero, R.; Verdú Martín, GJ. (2014). Desarrollo de un código neutrónico de difusión 2D y 3D estacionario por el Método de Volúmenes Finitos. Sociedad Nuclear Española. http://hdl.handle.net/10251/71941

Evaluation of the response of a Bonner Sphere Spectrometer with a (LiI)-Li-6 detector using 3D meshed MCNP6.1.1 models

[EN] In order to undertake further studies on neutron spectra deconvolution in radiotherapy LinAc bunkers after using high megavolts treatment beams, it has been calculated the theoretical Response Function for a widespread neutron Bonner Sphere Spectrometer (BSS) exposed to arbitrary neutron sources. The neutron response function of the Bonner spectrometer is of essential importance for its neutron spectrum unfolding procedure and is directly related to the quality of the unfolded spectrum. Response detector curves from 10 keV to 20 MeV have been obtained by Monte Carlo (MC) simulation with MCNP6.1.1, where the use of unstructured mesh geometries is introduced as a novelty. In order to validate the accuracy of the MCNP6 simulation, we have used the detector model to measure an 241Am-Be neutron source, and the obtained neutron counts of the spectrometer and simulated counts are found to be very consistent, with a relative error below 10%. This comparison shows that the estimation of the Bonner sphere neutron response by MCNP6 is highly precise.Morató-Rafet, S.; Juste Vidal, BJ.; Miró Herrero, R.; Verdú Martín, GJ.; Guàrdia, V. (2019). Evaluation of the response of a Bonner Sphere Spectrometer with a (LiI)-Li-6 detector using 3D meshed MCNP6.1.1 models. Radiation Physics and Chemistry. 155:221-224. https://doi.org/10.1016/j.radphyschem.2018.05.027S22122415