Resonance Treatment Innovations for Efficiency and Accuracy Enhancement in Direct Whole Core Calculations of Water-Cooled Power Reactors

Abstract

Innovations are introduced to the conventional resonance treatment in order to enhance the solution accuracy and the calculation efficiency of it in the direct whole core calculations for power reactors. First, the causes for yielding consistent biases in the resonance reaction rates are investigated. There are two causes which have been overlooked in the multi-group approach, but it turns out that the effect of the two causes leads to significant reactivity errors. Second, errors caused by the strategy to efficiently implement the subgroup method are figured out. The methods for removing these biases and errors resulting from each cause are then devised. On top of that, the calculation efficiency is greatly improved by reducing the number and the size of subgroup fixed source problems (SGFSPs) significantly which are needed to measure the self-shielding effect in each resonant region.<br/> The first overlooked cause is identified as the neglect of the angle dependency of multi-group cross sections in the resonance energy range. It is demonstrated that resonance absorption reaction rates are significantly over-estimated by ignoring the angle dependency in all kinds of multi-group transport codes. In order to resolve this problem, a new practical method is developed by parametrizing spectral superhomogenization factors over various pin-cell characteristics. <br/> The second overlooked cause is identified as the neglect of the temperature dependency of the hydrogen scattering kernel of the 0th Legendre order in the low epithermal energy range. It is identified that this neglect induces the under-estimation of spectrum in the low epithermal energy range, and thus, the under-estimation of resonance absorption reaction rates by the low-lying resonances. The physical reason for this is thoroughly investigated and a resolution based on pre-generated Monte Carlo solutions is derived. <br/> The strategic cause for the reactivity error is related with the reduction of the number of SGFSPs in the conventional scheme that used the concept of resonance categories and escape cross section interpolation. This problem is resolved in a way to effectively reduce the number of SGFSPs by developing the so-called macro level grid scheme. The need for constructing a SGFSP for each representative resonant isotope per category and for each of the four microscopic subgroup levels is eliminated by the macro level grid scheme. The reasoning for using the macroscopic levels is derived first and the way to determine the optimum macro levels is investigated. It is demonstrated that the macro level grid method requires only eight SGFSPs per energy group regardless of the number of resonant isotopes in a core. This macro level grid method is elaborated to work fine in non-uniform intra-pellet temperature and number density profile conditions.<br/> As the second measure to enhance noticeably the calculation efficiency of the SGFSPs, the equivalent Dancoff-factor cell model is applied. The strategy is to reduce the size of the SGFSPs by simplifying the geometry from the original two-dimensional entire core to a set of equivalent one-dimensional pin cells which preserve their own Dancoff factors. Using this strategy is reasonable because it does not involve any bias on effective cross sections because subgroup parameters can retrieve them having the exact heterogeneous geometry effect and the slowing down effect. The pin-wise Dancoff factors are obtained by using the enhanced neutron current method only once. The macro level grid method and the equivalent Dancoff-factor cell model are justified through illustrations on the physical reasons by a series of numerical experiments.<br/> As the result of this research, the integrated resonance treatment system is established with the innovated subgroup method resulting in significant computing time reduction and accuracy enhancement. It is proved that, by considering the exact physics in play which have been neglected, reactivity errors become less than 100 pcm for a variety of steady-state problems and a burnup rate, a fuel temperature coefficient and a global core power distribution are improved. Its fastness is demonstrated by the fact that the time portion of the resonance treatment among the total calculation time is greatly reduced from about 25% to less than 1%. This is the very attractive feature for the direct whole core calculation of power reactors where repeated resonance calculations are essential due to T/H feedback.<br/>