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
keff calculated with the finite mesh spacing method can be expressed approximately as
-δ
k(
Δr, Δz) ≡
k -
kD(
Δr, Δz) ?? -[(
Δr)
2 (
c1ρ +
c2) + (
Δz)
2 (
c3ρ +
c4)],
where
k and
kD (
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, δ
k 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Δk for the state with all control rods fully withdrawn or 1.9%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 δ
k'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z mesh model overestimates the power near the midplane of the core with all control rods fully withdrawn (inserted), by 01.6% (03.9%) in the inner core and by 03.7% (04. 8%) in the radial blanket, but underestimates it by 01.4% (01.6%) in the outer core, compared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.
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