Multi-group SP 3 approximation for simulation of a three-dimensional PWR rod ejection accident Deokjung Lee a,⇑ , Tomasz Kozlowski b , Thomas J. Downar c a Ulsan National Institute of Science and Technology, School of Mechanical and Nuclear Engineering, UNIST-gil 50, Eonyang-eup, Ulju-gun, Ulsan 689-798, Republic of Korea b University of Illinois at Urbana-Champaign, Department of Nuclear, Plasma, and Radiological Engineering, 216 Talbot Laboratory, Urbana, IL 61801, United States c University of Michigan, Department of Nuclear Engineering and Radiological Sciences, Ann Arbor, MI 48105, United States article info Article history: Received 19 March 2014 Received in revised form 16 August 2014 Accepted 21 October 2014 Keywords: SP 3 Pin-by-pin Full-core PARCS MOX abstract Previous researchers have shown that the simplified P 3 (SP 3 ) approximation is capable of providing suf- ficiently high accuracy for both static and transient simulations for reactor core analysis with consider- ably less computational expense than higher order transport methods such as the discrete ordinate or the full spherical harmonics methods. The objective of this paper is to provide a consistent comparison of two-group (2G) and multi-group (MG) diffusion and SP 3 transport for rod ejection accident (REA) in a practical light water reactor (LWR) problem. The analysis is performed on two numerical benchmarks, a3  3 assembly mini-core and a full pressurized water reactor (PWR) core. The calculations were per- formed using pin homogenized and assembly homogenized cross sections for a series of benchmarks of increasing difficulty, in two-dimensional (2D) and three-dimensional (3D), 2G and MG, diffusion and transport, as well as with and without feedback. All results show consistency with the reference results obtained from higher-order methods. It is demonstrated that the analyzed problems show small group- homogenization effects, but relatively significant transport effects which are satisfactorily addressed by the SP 3 transport method. The sensitivity tests also show that, for the REA simulation, the MG is more conservative than 2G, P 1 is more conservative than SP 3 for a 1/3 MOX loaded full-core problem. Ó 2014 Elsevier Ltd. All rights reserved. 1. Introduction For several decades the diffusion approximation has success- fully been applied for the analysis of the current generation of LWRs. For spatial discretization, advanced nodal methods such as the nodal expansion method (NEM) (Finnemann et al., 1977), the analytic nodal method (ANM) (Smith, 1979), the nodal integration method (NIM) (Fisher and Finnemann, 1981) and the analytic func- tion expansion method (AFEN) (Noh and Cho, 1993) have been used successfully to design and analyze several generations of reactors. These methods have been able to predict fuel pin-powers within a few percent of measured data using assembly size compu- tational mesh with some type of ‘‘pin-power reconstruction’’ technique. However, there has been a concern that the methods which were developed and benchmarked primarily for Uranium fueled LWRs do not perform equally well when applied to mixed oxide (MOX) fuelled cores or other cores with a very heterogeneous fuel loading. Several researchers have identified the specific approxi- mations that contribute to the errors observed in the nodal meth- ods. Systematic analysis has isolated deficiencies in four basic categories: a spatial discretization effect, a spatial homogenization effect, a group collapsing effect, and a transport effect (Downar et al., 2000, 2002; Lee et al., 2002). Because of these issues, the neutronics methods in the U.S. NRC neutron kinetics code PARCS (Purdue Advance Reactor Core Simu- lator) (Downar et al., 2002) were improved for the transient anal- ysis of LWR cores with MOX fuel. There was concern that the conventional 2G nodal methods could not properly treat partially fueled MOX cores which have large flux gradients at the interface of MOX and uranium-oxide (UOX) fuel assemblies. Downar et al. assessed the impact of MOX loading on the accuracy of the conven- tional 2G nodal approaches in PARCS based on the various approx- imations used to solve the Boltzmann transport equation: assembly homogenization, spatial discretization, group collapsing, transport effect and spatial dehomogenization (Downar et al., 2000). Subsequent research efforts addressed these issues and this paper summarizes the improvements in the PARCS methodology for MOX steady-state and transient core analysis. http://dx.doi.org/10.1016/j.anucene.2014.10.019 0306-4549/Ó 2014 Elsevier Ltd. All rights reserved. ⇑ Corresponding author. Tel.: +82 52 217 2940, +82 10 2863 6255; fax: +82 52 217 3008. E-mail address: deokjung.lee@gmail.com (D. Lee). Annals of Nuclear Energy 77 (2015) 94–100 Contents lists available at ScienceDirect Annals of Nuclear Energy journal homepage: www.elsevier.com/locate/anucene