AFEN-polynomial correction model for reactor cores with fuel assemblies under burnup gradients

Abstract

In this thesis, a new burnup correction model for the AFEN (Analytic Function Expansion Nodal) method is developed and applied to two-dimensional, two-group neutron diffusion problems in rectangular geometry. In this model, the intranodal flux distribution of the burnt fuel assembly is expanded in a combination of analytic basis functions and additional polynomial correction terms, while only analytic basis functions are used for homogeneous assemblies. The analytic basis functions are obtained using the volume-averaged group constants of the burnt assembly and low order (first or second order) polynomials are used as the correction terms. As in the homogeneous AFEN, all the expansion coefficients of flux distribution are expressed in terms of nine nodal quantities (one node average flux, four surface average fluxes, four corner point fluxes) in two-dimensional rectangular geometry. For a burnt fuel assembly, the number of expansion coefficients is larger than that of nodal unknowns because of the polynomial correction terms. The additional conditions to determine the coefficients of the correction terms are obtained using a weighted residual method. This burnup correction model does not require additional discontinuity factors and flux-volume-weighted cross sections, which are, however, needed in the rehomogenization model (that rehomogenizes the burnt fuel assembly using equivalence theory). Therefore, the newly developed method is free from uncertainty of rehomogenization. The new burnup correction model was implemented and the capability to treat the intranodal cross section gradients was tested on several benchmark problems. The results show that the model developed in this study eliminates almost all the errors in the nodal unknowns which are induced by the intranodal burnup gradients. Also we note that the first order polynomial correction can provide accurate solutions even for a steep burnup gradient and that additional accuracy is obtained from the se...