Parameterized representation of macroscopic cross section in burn-up cycles João Claudio B. Fiel ⇑ , Thiago F. Belo Department of Nuclear Engineering, Military Institute of Engineering, Rio de Janeiro, Brazil article info Article history: Received 28 January 2016 Received in revised form 11 April 2016 Accepted 15 April 2016 Available online 23 April 2016 Keywords: Cross section SCALE Tchebyshev Parameterization abstract Nuclear reactor core analysis involves neutronic modeling and the calculations require problem depen- dent nuclear data generated with few neutron energy groups, as for instance the neutron cross sections. The methods used to obtain these problem-dependent cross sections, in the reactor calculations, generally uses nuclear computer codes that require a large processing time and computational memory, making the process computationally very expensive. To provide the cross sections of rapidly and without the dependence of complex systems calculations, this work developed a set of parameterized macro- scopic cross sections, based on the Tchebychev polynomials, by fitting the cross sections as a function of nuclear parameters, which include fuel temperature, moderator temperature and density. In this study is evaluated the problem-dependent about fission, scattering and capture cross sections for a typical PWR fuel element reactor, considering burn-up cycles. The analysis was carried out with the SCALE 6.1 code package. Tests realized as the temperature coefficient of reactivity, fast fission factor, and the comparison with direct calculations with the SCALE code system and with Lagrange polynomials show excellent agreements. The differences between the cross section parameterization methodology and the direct calculations based on the SCALE code system are less than 0.03%. Ó 2016 Elsevier Ltd. All rights reserved. 1. Introduction The nuclear reactor design is based on control of several vari- ables. These variables include the nature of the fuel and the mod- erator, core compositions and geometry, and removal of the heat which is generated mainly by fission and partly by radioactive decay. An essential part of the reactor design is the core specifica- tion, since this determines the neutron behavior in the system and hence the criticality conditions (Glasstone and Sesonske, 1994). Neutronic calculations are based on either transport or diffusion theory, which can be implemented by deterministic or stochastic method (Monte Carlo). In general the calculations require problem dependent nuclear data generated with few neutron energy groups, as for instance the neutron cross sections, which depend on the fuel element material composition as well as the thermal hydraulic parameters. During the reactor operation the fuel com- position will change as fissile isotopes are consumed and fissions products are produced, resulting in a different behavior of the absorption cross section. These changes, in both space and time, which occur in the composition of the fuel, can be determinate by the fuel burn-up calculation. Presently, analysis and studies of the macroscopic cross section, as a function of nuclear parameters, have shown very distinct behavior that cannot be represented by simply using linear inter- polation. Indeed, a polynomial representation is more adequate for the data parameterization. Nevertheless, existing methods do not indicate explicitly the type of polynomial fit that best repre- sents the problem-dependent cross section. The methods used to obtain these problem-dependent cross sections, in the reactor cal- culations, generally uses nuclear computer codes that require a large processing time and computational memory, making the pro- cess computationally very expensive. Therefore, new methods have been studied for the purpose of seeking alternative proce- dures to provide the cross sections of rapidly and safely without the dependence of complex systems calculations. Over the years, methods of few-groups cross section parameterization using math- ematical processes such as stepwise regression (Zimin and Semenov, 2005), quasi-regression (Bokov, 2009) and sparse grids methods (Prinsloo et al., 2009), were elaborated and suggested. It was developed (Fiel, 2013) a study of the cross section parameterization using Tchebychev polynomials based on problem dependent cross sections calculated with the SCALE code system for the zero cycle condition, i.e., the fresh PWR reactor. This http://dx.doi.org/10.1016/j.anucene.2016.04.025 0306-4549/Ó 2016 Elsevier Ltd. All rights reserved. ⇑ Corresponding author. E-mail addresses: fiel@ime.eb.br (J.C.B. Fiel), thiagofreitasbelo@gmail.com (T.F. Belo). Annals of Nuclear Energy 94 (2016) 472–477 Contents lists available at ScienceDirect Annals of Nuclear Energy journal homepage: www.elsevier.com/locate/anucene