Consistent hybrid diffusion-transport spatial homogenization method

Abstract

Recent work by Yasseri and Rahnema has introduced a consistent spatial homogenization (CSH) method completely in transport theory. The CSH method can very accurately reproduce the heterogeneous flux shape and eigenvalue of a reactor, but at high computational cost. Other recent works for homogenization in diffusion or quasi-diffusion theory are accurate for problems with low heterogeneity, such as PWRs, but are not proven for more heterogeneous reactors such as BWRs or GCRs.

To address these issues, a consistent hybrid diffusion-transport spatial homogenization (CHSH) method is developed as an extension of the CSH method that uses conventional flux weighted homogenized cross sections to calculate the heterogeneous solution. The whole-core homogenized transport calculation step of the CSH method has been replaced with a whole- core homogenized diffusion calculation. A whole-core diffusion calculation is a reasonable replacement for transport because the homogenization procedure tends to smear out transport effects at the core level. The CHSH solution procedure is to solve a core-level homogenized diffusion equation with the auxiliary source term and then to apply an on-the-fly transport-based re-homogenization at the assembly level to correct the homogenized and auxiliary cross sections. The method has been derived in general geometry with continuous energy, and it is implemented and tested in fine group, 1-D slab geometry on controlled and uncontrolled BWR and HTTR benchmark problems. The method converges to within 2% mean relative error for all four configurations tested and has computational efficiency 2 to 4 times faster than the reference calculation.