Analytical Dancoff factor evaluations for reactor designs loaded with TRISO particle fuel

Abstract

A new mathematical model, the dual-sphere model, is proposed to analytically evaluate Dancoff factors of TRISO fuel kernels based on the chord method. The accurate evaluation of fuel kernel Dancoff factors is needed when one analyzes nuclear reactors loaded with TRISO particle fuel. In these reactor designs, fuel kernels are randomly distributed and shield each other, causing a shadowing effect. The Dancoff factor is a quantitative measure of this effect and is determined by the spatial distribution of fuel kernels. A TRISO fuel particle usually consists of four layers that form a coating region outside the fuel kernel. When fuel particles are loaded in the reactor, the spatial distribution of fuel kernels can be affected by the thickness of the coating region. Therefore, the coating region should be taken into account in the calculation of Dancoff factors. However, the previous model, the single-sphere model, assumes no coating regions in the Dancoff factor predictions. To address this model deficiency, the dual-sphere model is proposed by deriving a new chord length distribution function between two fuel kernels that explicitly accounts for coating regions. The new model is employed to derive analytical solutions of infinite medium, intra-fuel pebble and intra-fuel compact/pin Dancoff factors over a wide range of volume packing fractions of TRISO fuel particles, varying from 2% to 60%. Comparisons are made with the predictions from the single-sphere model and reference Monte Carlo simulations. A significant improvement of the accuracy, over the ranges of packing fractions under current investigation, has been observed. The new model provides a reliable numerical evaluation of Dancoff factors for TRISO particle fuel and can be used as a routine method for the neutronic design and analysis of reactors loaded with TRISO particle fuel.