Calculating the effective delayed neutron fraction in the Molten Salt Fast Reactor: Analytical, deterministic and Monte Carlo approaches

•Calculation of effective delayed neutron fraction in circulating-fuel reactors.•Extension of the Monte Carlo SERPENT-2 code for delayed neutron precursor tracking.•Forward and adjoint multi-group diffusion eigenvalue problems in OpenFOAM.•Analytical approach for βeff calculation in simple geometries and flow conditions.•Good agreement among the three proposed approaches in the MSFR test-case.

This paper deals with the calculation of the effective delayed neutron fraction (βeff) in circulating-fuel nuclear reactors. The Molten Salt Fast Reactor is adopted as test case for the comparison of the analytical, deterministic and Monte Carlo methods presented. The Monte Carlo code SERPENT-2 has been extended to allow for delayed neutron precursors drift, according to the fuel velocity field. The forward and adjoint eigenvalue multi-group diffusion problems are implemented and solved adopting the multi-physics tool-kit OpenFOAM, by taking into account the convective and turbulent diffusive terms in the precursors balance. These two approaches show good agreement in the whole range of the MSFR operating conditions. An analytical formula for the circulating-to-static conditions βeff correction factor is also derived under simple hypotheses, which explicitly takes into account the spatial dependence of the neutron importance. Its accuracy is assessed against Monte Carlo and deterministic results. The effects of in-core recirculation vortex and turbulent diffusion are finally analysed and discussed.