Time-dependent neutron diffusion coefficient for the effective diffusion equation

Abstract The time-dependency of neutron diffusion coefficient as well as neutronic interfacial coefficients in nuclear reactors at short time-scale is investigated via the volume averaging method. The boundary-value problems of governing differential equation for spatial deviations around averages of local variables are developed in this work. The general solution of spatial deviations-boundary-value problem allows closing the up-scaled neutron diffusion equation, which incorporates new terms with respect to classic equation. Meanwhile, the particular solutions of spatial deviations enable the numerical estimation of effective diffusion and neutronic interfacial coefficients. The geometrical domains where effective coefficients were numerically computed include 2D and 3D unit cells, which are representative geometries for two types of nuclear reactors: conventional arrangements with fuel rods and pebble bed. The numerical estimations were fitted to an analytical expression as function of time. The numerical solution of up-scaled model and comparison with results of direct numerical simulations are presented and discussed in this work.