Development and Verification of Nuclear Calculation Methods for ...

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tributed uniformly within the sing.« cells, and extended to the multi-group
scheme for the cell flux calculation they account for the surrounding lattice.
At the end of the time step, macroscopic homogenized few-group cross
sections are determined for the individual cells from the distributions of
spatial flux spectrum and isotopic number densities within the cells by
means of a multi-group microscopic cross section library.
Then follows a few-group, two-dimensional diffusion theory calculation,
which provides local power densities and neutron leakage spectra for
the single cells during the next time step repeating the whole process.
During each time step the power density and neutron leakage over-all
distributions as well as the flux spectrum within the individual cells are assumed
to be invariant.
Some iterations between cell and over-all reactor calculation are usually
necessary to establish the proper (converged) effect and flux spectrum
conditions thus ensuring the true surroundings for the fuel rods during the
irradiation.
8.2. Non-Uniform Doppler and Dancoff Effects
The heterogeneity of the lattice from the presence of water gaps, nonuniform
local enrichments for power flattening and self-shielded burnable
poison in the fuel makes local spatial neutron spectrum variations important.
However, the applied microscopic cross sections for determination of
these variations are spatially dependent.
The spatial variation in power density changes the capture rate espe-
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cially in the U and Pu resonances. This non-uniform Dopplcr broadening
effect is accounted for by means of a simple linear interpolation with
microscopic absorption cross sections for U 238 and Pu 2 *" as functions of
powei density. The cell burn-up calculations are, therefore, at each time
step provided with microscopic absorption cross sections for IT and
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Pu depending on the previously determined local power densities.
For correct establishment of the (converged) over-all power density
distribution some iterations are normally required with time steps of zero
length.
The Dancoff interaction effect varies locally throughout the fuel assembly.
Corner and face fuel rods near water gaps are not shielded as
much as asymptotic rods by neighbouring fuel rode, and they consequently
have a Dancoff factor closer to zero. This non-uniform Dancoff effect is