Spatial Mesh Effect in Three-Dimensional Diffusion Calculations for Fast Reactors

抄録

A correction to the numerical solution of the diffusion equation solved using the finite mesh spacing method has been studied for a fast breeder reactor. It has been found that the correction to the effective multiplication factor k_eff calculated with the finite mesh spacing method can be expressed approximately as
-δk(Δr, Δz) ≡ k - k_D(Δr, Δz) ?? -[(Δr)² (c_1ρ +c₂) + (Δz)² (c_3ρ +c₄)],
where k and k_D (Δr, Δz) are, respectively, the eigenvalues of the diffusion equation and its approximate finite difference equation with mesh spacings ΔrJr in the x-y plane and Δz along the z axis. The quantity ρ is the total reactivity worth of control rods inserted into the core. The constants c₁, c₂, c₃ and c₄, are determined from the geometrical shape and atomic densities of constituent materials of a reactor core.
For a prototype LMFBR, δk with Δr = Δz = 11.5 cm (hexagonal-z mesh model) amounts to 0.8%Δk for the state with all control rods fully withdrawn or 1.9%Δk for the state with control rods fully inserted. The δk's with Δr = Δz = 3.83 cm (triangular-z mesh model) are less than 0.23%Δk for various patterns of the control rods. As for the power distribution, the hexagonal-z mesh model overestimates the power near the midplane of the core with all control rods fully withdrawn (inserted), by 01.6% (03.9%) in the inner core and by 03.7% (04. 8%) in the radial blanket, but underestimates it by 01.4% (01.6%) in the outer core, compared with that from the triangular mesh model.