Spatial mesh effect in three-dimensional diffusion calculations for fast reactors.
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概要
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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 <I>k</I><SUB>eff</SUB> calculated with the finite mesh spacing method can be expressed approximately as<BR>-δ<I>k</I>(<I>Δr, Δz</I>) ≡ <I>k</I> - <I>k<SUB>D</SUB></I>(<I>Δr, Δz</I>) ?? -[(<I>Δr</I>)<SUP>2</SUP> (<I>c</I><SUB>1ρ</SUB> +<I>c</I><SUB>2</SUB>) + (<I>Δz</I>)<SUP>2</SUP> (<I>c</I><SUB>3ρ</SUB> +<I>c</I><SUB>4</SUB>)], <BR>where <I>k</I> and <I>k<SUB>D</SUB></I> (<I>Δr, Δz</I>) are, respectively, the eigenvalues of the diffusion equation and its approximate finite difference equation with mesh spacings <I>Δr</I>Jr in the <I>x</I>-<I>y</I> plane and <I>Δz</I> along the <I>z</I> axis. The quantity ρ is the total reactivity worth of control rods inserted into the core. The constants <I>c</I><SUB>1</SUB>, <I>c</I><SUB>2</SUB>, <I>c</I><SUB>3</SUB> and <I>c</I><SUB>4</SUB>, are determined from the geometrical shape and atomic densities of constituent materials of a reactor core.<BR>For a prototype LMFBR, δ<I>k</I> with <I>Δr</I> = <I>Δz</I> = 11.5 cm (hexagonal-<I>z</I> mesh model) amounts to 0.8%<I>Δk</I> for the state with all control rods fully withdrawn or 1.9%<I>Δk</I> for the state with control rods fully inserted. The δ<I>k</I>'s with <I>Δr</I> = <I>Δz</I> = 3.83 cm (triangular-<I>z</I> mesh model) are less than 0.23%<I>Δk</I> for various patterns of the control rods. As for the power distribution, the hexagonal-<I>z</I> mesh model overestimates the power near the midplane of the core with all control rods fully withdrawn (inserted), by 01.6% (03.9%) in the inner core and by 03.7% (04. 8%) in the radial blanket, but underestimates it by 01.4% (01.6%) in the outer core, compared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.
- 一般社団法人 日本原子力学会の論文
著者
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TAKEDA Seiichi
Energy Research Laboratory, Hitachi, Ltd.
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TAKEDA Seiichi
Energy Research Laboratory, Hitachi Ltd.
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SAKAGAMI Masaharu
Energy Research Laboratory Hitachi Ltd.
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