Monte Carlo methodologies for neutron streaming in diffusion calculations - Application to directional diffusion coefficients and leakage models in XS generation

Thumbnail Image
Journal Title
Journal ISSN
Volume Title
School of Science | Doctoral thesis (article-based) | Defence date: 2016-05-18
Degree programme
89 + app. 66
Aalto University publication series DOCTORAL DISSERTATIONS, 60/2016
Neutron transport calculations by Monte Carlo methods are finding increased application in nuclear reactor simulations. In particular, a versatile approach entails the use of a 2-step procedure, with Monte Carlo as a few-group cross section data generator at lattice level, followed by deterministic multi-group diffusion calculations at core level. In this thesis, the Serpent 2 Monte Carlo reactor physics burnup calculation code is used in order to test a set of diffusion coefficient models, as well as neutron leakage methodologies at assembly level. The tests include novel anisotropic diffusion coefficient and heterogeneous leakage models developed and implemented by the author. The analyses are mainly focused on a sodium-cooled fast reactor system, for which few-group cross section data was generated by stochastic methods with Serpent 2. The quality of the full-core diffusion results is evaluated by contrasting system eigenvalues and power distributions against detailed, full-core reference solutions also supplied by the Serpent 2 code and the same nuclear data library. Whereas the new anisotropic diffusion coefficient formalism exhibits improved performance in the fast reactor system studied, there are restrictions to its applicability in other reactor designs. The newly proposed leakage model has a similar performance to that one of albedo ite-rations, and provides valuable information about the space-energy coupling of the scalar neutron flux at lattice level. This hitherto unavailable information does not entail a significant computational cost. In sodium-cooled fast reactor calculations, the quality of diffusion theory results can be improved by either using directional diffusion coefficients and a fine energy mesh, or via leakage-corrected discontinuity factors. These factors can be calculated using net neutron currents supplied by heterogeneous leakage models. Preliminary results from this research also suggest that the studies maybe extended to graphite-moderated, gas-cooled reactors.
Supervising professor
Tuomisto, Filip, Prof., Aalto University, Department of Applied Physics, Finland
Thesis advisor
Leppänen, Jaakko, Adj. Prof., VTT Technical Research Centre of Finland Ltd, Finland
Monte Carlo, Serpent, directional diffusion coefficient, TRIZ, TRIVAC, neutron leakage, layer expansion, albedo, B1, discontinuity factor, SFR
Other note
  • [Publication 1]: E. Dorval.2014. A New Method for the Calculation of Diffusion Coefficients with Monte Carlo. In Proceedings of the Joint International Conference on Supercomputing in Nuclear Applications and Monte Carlo 2013 (SNA + MC 2013), Paris, 02204,
    DOI: 10.1051/snamc/201402204 View at publisher
  • [Publication 2]: E. Dorval and J. Leppänen.2015. Monte Carlo current-based diffusion coefficients: Application to few-group constants generation in Serpent. Annals of Nuclear Energy, 78, pp. 104–116,
    DOI: 10.1016/j.anucene.2014.12.011 View at publisher
  • [Publication 3]: E. Dorval. 2016. Directional diffusion coefficients and leakage-corrected discontinuity factors: Implementation in Serpent and tests. Annals of Nuclear Energy, 87, pp. 101–112,
    DOI: 10.1016/j.anucene.2015.08.019 View at publisher
  • [Publication 4]: E. Dorval. 2016. A Comparison of Monte Carlo methods for neutron leakage at assembly level. Annals of Nuclear Energy, 87, pp. 591–600,
    DOI: 10.1016/j.anucene.2015.10.014 View at publisher
  • [Publication 5]: E. Dorval. 2016. A comparative study of leakage and diffusion coefficient models for few-group cross section generation with the Monte Carlo method. Annals of Nuclear Energy, 90, pp. 353–363,
    DOI: 10.1016/j.anucene.2015.12.021 View at publisher