Abstract
The development of a new computational framework for core multi-physics problems, called Kraken, has been started at VTT Technical Research Centre of Finland Ltd. The framework consists of modular neutronics, thermal hydraulics and thermal mechanics solvers, and is based on the use of continuous-energy Monte Carlo reactor physics program Serpent. Ants is a new reduced order nodal neutronics program developed as a part of Kraken. The published methodology and first results of Ants has previously been limited to rectangular geometry steady state multigroup diffusion solutions. This work describes the solution methodology of Ants extended to hexagonal geometry steady state diffusion solutions. The first results using various two-dimensional and three-dimensional hexagonal geometry numerical benchmarks are presented. These benchmarks include the AER-FCM-001 and AER-FCM-101 three-dimensional VVER-440 and VVER-1000 mathematical benchmarks. The obtained effective multiplication factors of all considered benchmarks are within 18 pcm and the RMS relative assembly power relative differences are within 0.4% of the reference solutions.
Kurzfassung
Am finnischen VTT Forschungszentrum wurde mit der Entwicklung eines neuen Frameworks zur Berechnung von multiphysikalischen Reaktorkernaufgabenstellungen, genannt Kraken, begonnen. Das Framework besteht aus modularen Neutronenkinetik-, Thermohydraulik- und Thermomechanik-Lösern und basiert auf dem Monte-Carlo-Reaktorphysikprogramm Serpent. Dabei wurde als Teil von Kraken das Programm Ants zur Berechnung der Neutronenkinetik durch nodale Lösung von Differentialgleichungen reduzierter Ordnung entwickelt. Ants war bisher auf die Lösung der stationären Mehrgruppendiffusionsgleichung für rechteckige Geometrie beschränkt. In diesem Beitrag wird die Erweiterung der Lösungsmethodik von Ants beschrieben, mit der nun auch Diffusionslösungen in hexagonalen Kerngeometrien beschrieben und berechnet werden können. Die ersten Ergebnisse mit verschiedenen zweidimensionalen und dreidimensionalen numerischen Benchmarks für hexagonale Geometrie werden vorgestellt. Zu diesen Benchmarks gehören die dreidimensionalen mathematischen Benchmarks AER-FCM-001 und AER-FCM-101 für VVER-440 und VVER-1000. Die erhaltenen effektiven Multiplikationsfaktoren aller betrachteten Benchmarks liegen innerhalb von 18 pcm und die relativen Unterschiede der Brennelementleistung liegen innerhalb von 0,4% der Referenzlösungen.
References
1 Leppänen, J.; Pusa, M.; Viitanen, T.; Valtavirta, V.; Kaltiaisenaho, T.: The Serpent Monte Carlo code: Status, development and applications in 2013. Annals of Nuclear Energy82 (2015) 142–15010.1016/j.anucene.2014.08.024Search in Google Scholar
2 Leppänen, J.; Pusa, M.; Fridman, E.: Overview of methodology for spatial homogenization in the Serpent 2 Monte Carlo code. Annals of Nuclear Energy96 (2016) 126–13610.1016/j.anucene.2016.06.007Search in Google Scholar
3 Sahlberg, V.; Rintala, A.: Development and first results of a new rectangular nodal diffusion solver of Ants. In proc. PHYSOR 2018. (2018)Search in Google Scholar
4 Noh, J. M.; Cho, N. Z.: A new approach of analytic basis function expansion to neutron diffusion nodal calculation. Nuclear Science and Engineering116 (1994) 165–18010.13182/NSE94-A19811Search in Google Scholar
5 Xia, B.; Xie, Z.: Flux expansion nodal method for solving multigroup neutron diffusion equations in hexagonal-z geometry. Annals of Nuclear Energy33 (2006) 370–37610.1016/j.anucene.2005.06.011Search in Google Scholar
6 Cho, N. Z.; Kim, Y. H.; Park, K. W.: Extension of analytic function expansion nodal method to multigroup problems in hexagonal-z geometry. Nuclear Science and Engineering126 (1997) 35–4710.13182/NSE97-A24455Search in Google Scholar
7 Woo, S. W.; Cho, N. Z.; Noh, J. M.: The analytic function expansion nodal method refined with transverse gradient basis functions and interface flux moments. Nuclear Science and Engineering 139.2 (2001) 156–17310.13182/NSE01-A2229Search in Google Scholar
8 Lawrence, R. D.: The DIF3D nodal neutronics option for two- and three-dimensional diffusion theory calculations in hexagonal geometry. ANL-83-1. Argonne National Laboratory, 198310.2172/6318594Search in Google Scholar
9 Benchmark Problem Book. ANL-7416 Supplement 2. Argonne National Laboratory, 1977Search in Google Scholar
10 Chao, Y.; Shatilla, Y.: Conformal mapping and hexagonal nodal methods–II: implementation in the ANC-H code. Nuclear Science and Engineering121 (1995) 210–22510.13182/NSE95-A28559Search in Google Scholar
11 Makai, M.: Response matrix of symmetric nodes. Nuclear Science and Engineering86 (1984) 302–31410.13182/NSE84-A17559Search in Google Scholar
12 Makai, M.: Diffusion theoretical investigations of the physical properties of uranium-water lattices. Final Report of TIC. Vol. 5. Akadémiai Kiadó, 2000Search in Google Scholar
13 Singh, K.; Kumar, V.: Solution of the multigroup diffusion equation in hex-z geometry by finite Fourier transformation. Annals of Nuclear Energy20 (1993) 153–16110.1016/0306-4549(93)90098-ASearch in Google Scholar
14 Beckert, C.; Grundmann, U.: Entwicklung einer Transportnährung für das reaktordynamische Rechenprogramm DYN3D. In German. FZD-497. Forschungszentrum Dresden-Rossendorf Institut für Sicherheitsforschung, 2008Search in Google Scholar
15 Maráczy, C.; Kolev, N. P.; Magnaud, C.; Lenain, R.: AER Benchmark Specification Sheet. 1999. URL: http://aerbench.kfki.hu/aerbench/FCM001.doc (accessed Sept. 20, 2018)Search in Google Scholar
16 Maráczy, C.: A solution of Seidel's 3-D benchmark for VVER-440 with the DIF3D-FD code. In proc. the fifth Symposium of AER. (1995)Search in Google Scholar
17 Kolev, N. P.; Lenain, R.; Magnaud, C.: AER Benchmark Specification Sheet. 1999. URL: http://aerbench.kfki.hu/aerbench/FCM101.doc (accessed Sept. 20, 2018)Search in Google Scholar
© 2019, Carl Hanser Verlag, München
