A Comparison Between Recent Advances in Cylindrical Nodal Diffusion Methods

The resurgence of high temperature reactor (HTR) technology has prompted the development and application of modern calculation methodologies, many of which are already utilized in the existing power reactor industry, to HTR designs. To this end, the use of nodal diffusion methods for full core neutronic analysis is once again considered for both their performance and accuracy advantages. Recently a number of different approaches to two-dimensional and 3D multigroup cylindrical nodal diffusion methods were proposed by various institutions for use in HTR and, specifically, pebble-bed modular reactor (PBMR) calculations. In this regard, we may mention the NEM code from the Pennsylvania State University based on the nodal expansion method and the OSCAR-4 code from NECSA, utilizing a conformal mapping approach to the analytic nodal method. In this work we will compare these two approaches in terms of accuracy and performance. Representative problems, selected to test the methods thoroughly, were devised and based on both a modified version of the PBMR 400 MW benchmark problem and a “cylindrisized” version of the IAEA two-group problem. The comparative results between OSCAR-4 and NEM are given, focusing on global reactivity estimation, as well as power and flux errors as compared with reference finite-difference solutions. These results indicate that both OSCAR-4 and NEM recover the global reference solution for the IAEA problem and show power errors, which are generally acceptable for nodal methods. For the PBMR problem the accuracy is similar, but some convergence difficulties are experienced at the outer boundaries of the system due to the very large dimensions of the reflector (when compared with typical water-moderated reactors). For both codes a significant performance increase was found, as compared with finite-difference calculations, which is the method currently employed by the PBMR (Pty) Ltd. In conclusion it seems that nodal methods have potential for use in the HTR analysis and, specifically, the PBMR calculational arena, although cylindrical geometry based nodal methods will have to develop toward maturity before becoming the industry standard.