Resonance Calculation Method Based on Energy Spectrum Using Reduced Order Model

Abstract

Resonance calculation is one of the most important and difficult parts of core analysis and can dominate the accuracy of the core analysis. There are three methods for resonance computation: ultra-fine group (UFG) method, equivalence method, and subgroup method. Each of the approaches has advantages and disadvantages. UFG method is suitable for rigorous resonance calculation of various reactors, but the efficiency is very low for complex geometry and large-scale core. The equivalent theory has high computational efficiency and is widely used in core calculations. But the equivalence theory uses many assumptions and approximations, and its accuracy and application are limited. Subgroup theory can efficiently calculate resonance self-shield effects for arbitrary geometric problems, but the potential drawback is the limitation on the treatment of the resonance interference effect and the nonuniform temperature distribution. In conclusion, conventional methods have difficulties on balancing the accuracy and efficiency. In this paper, it is proposed to use generalized group condensation theory and reduced order model to extract the features of energy spectra in resonance calculation. Based on the ultrafine group energy spectra under 40 different background sections, the orthogonal bases are generated using these energy spectra. Using singular value decomposition and low rank approximation, the orthogonal basis functions related to energy spectrum characteristics are generated. Based on generalized group condensation theory, the neutron transport equation is solved by orthogonal basis. By solving the broad group angular flux expansion coefficient that considers the weight of orthogonal basis function distribution, the ultra-fine group energy spectrum is reconstructed. Finally, the effective cross-section is calculated by using the ultra-fine group energy condensation. According to the JAERI benchmark, UO2 fuel cells and MOX fuel cells with different enrichments are designed as problems for this calculation. Numerical results show that the maximum relative error of the reconstructed effective cross-section is below 2% for each problem. The impact on accuracy of the effective cross-section and keff from different orthogonal orders are analyzed. It is found that for fuel cells with different enrichment, the minimum orthogonal order required to achieve sufficient accuracy is different. With the increase of orders, the computation time increases linearly. It is found that when the cumulative contribution rate of singular value reaches 99.9%, the fine energy spectrum can be accurately described. These results show that the Resonance calculation method based on the Energy Spectrum Reduction model (RESR) can effectively predict the resonance self-screen cross-section, and its computational efficiency has certain advantages.

Keywords

• resonance calculation
• effective section
• low-rank approximation
• reduced-order model