Advanced nodal methods for mixed oxide fuel analysis

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Nuclear Engineering, 1997.Includes bibliographical references (leaves 124-127).One method being considered for the disposal of surplus weapons grade plutonium is to bum the plutonium as mixed oxide fuel (MOX) in commercial light water reactors (LWR's). The introduction of MOX fuel into LWR's poses several challenges for the reactor analyst. The spectrum difference between MOX and U02 assemblies creates a large thermal flux gradient at the interface between these assemblies. Current nodal methods, which use a transverse leakage approximation, have difficulty modeling this gradient. In this thesis, an advanced nodal method is introduced which uses a two-dimensional, non-separable expansion of polynomial and hyperbolic functions to represent the two-group flux, rather than the transverse leakage approximation. The steep thermal flux gradient also introduces errors in the spatial cross section homogenization. The spatial flux shape used to generate two-group cross sections does not account for the steep gradient, and therefore, the cross sections may be inaccurate. In this thesis, the cross sections are dynamically homogenized using the actual flux shape found in the reactor configuration. This is done by using a consistent method of spatial homogenization derived directly from the assumption of homogeneous and heterogeneous flux separability. From this assumption, discontinuity factors, homogenized cross sections, and adjusted diffusion coefficients are derived which preserve heterogeneous reaction rates and currents in the nodal solution. The flux separability assumption also leads to a pin-power reconstruction method which is completely consistent with the homogenization procedure. Because MOX and U02 assembly cross sections are homogenized using infinite-medium spectra, MOX and U02 spectrum interactions introduce error into the spectral cross section homogenization. In the actual reactor configuration, the spectrum is a combination of MOX and U02 spectra, and single-assembly cross sections may be inaccurate. This problem is addressed by correcting the homogeneous cross sections with empirical correlations which account for spectral interactions. The methods outlined in this thesis are applied to several benchmark problems containing MOX and U02 assemblies. These benchmark problems show that the advanced nodal and homogenization methods derived in this thesis produce more accurate results than current analysis methods. With these advanced methods, reactor cores containing MOX fuel can be accurately analyzed using two-group nodal methods and single-assembly calculations.by Scott P. Palmtag.Ph.D