A New Homogenization Technique for Shielding Transport Calculations in Heterogeneous Regions

Abstract

A new homogenization technique for neutron cross section in the heterogeneous region has been developed for shielding transport calculations. The proposed homogenization technique consists of two steps. The first step is the flux weighting method, in which averaged cross sections are produced so as to conserve the reaction rates using the neutron flux obtained from the heterogeneous cell calculation. In the second step, the averaged cross section values obtained from the first step are adjusted in order that the gradient of the neutron flux in the homogeneous calculation using the adjusted cross section will agree with that in the heterogeneous cell calculation.

Calculated results of three homogenization techniques have been compared with that of heterogeneous calculation in the case of an LMFBR B4C axial shield. The volume weighting method, which is usually used in shielding design calculations, underestimates the total neutron flux by a factor of 4.0.

The flux weighting method, although providing a better approximation than the volume weighting method, still underestimates by a factor of 1.7. On the other hand, the proposed homogenization method shows good agreement with the heterogeneous calculation within an error of few percent. The proposed homogenization technique is shown to be effective in improving the accuracy of practical shielding transport calculations.

KEYWORDS:

• homogenization methods
• flux weighting
• neutron flux
• Volume weighting
• apjustment
• heterogeneous region
• SN method
• neutron transport
• transport calculation
• shielding design
• LMFBR type reactors
• axial shield