Cross-section homogenization using precomputed surface flux response matrices

It is well known that the use of exact discontinuity factors in the nodal method will not yield the correct (heterogeneous) node-averaged flux without the use of the exact assembly-averaged cross sections. (The word open-quotes exactclose quotes refers to values calculated from the solution to the fine-mesh heterogeneous problem.) Due to the core environmental effects (assembly surface leakage), these cross sections cannot be computed a priori. Several methods have been proposed to treat core environmental effects within the nodal calculations. Of particular interest is the net-current response matrix (NRM) method, which precomputed fixed-source calculations with net-current boundary conditions-were used to accurately rehomogenize the equivalence parameters (homogenized cross sections). The main weakness of this method is that the net-current response matrices do not exist for the case in which the estimated global (core) eigenvalue (keff) happens to be equal to the k∞ of the assembly (region) of interest. As a result, for the states near this singular condition, elements of net-current response matrices will approach positive or negative infinite, depending on which side (supercritical or subcritical) of the singularity they are on. In this paper, we have mitigated this problem by using the surface flux as the fixed-source boundary condition to generate the precomputed matrices. Since the generation of the surface flux response matrices (SFRM) requires no a priori knowledge of the actual boundary conditions, this method does not iterate between the nodal and lattice calculations. By using assembly-type dependent (precomputed) SFRMS, the homogenized cross sections for each node are computed directly within the nodal calculations. Preliminary results show that the SFRM method leads to more accurate nodal solutions when compared with the standard homogenization (SH) technique