Performance analysis of functional expansion tallies on 2D PWR pin cell

Abstract

Functional Expansion Tally (FET) method has been rigorously studied in recent years, as it has the potential to model spatial distributions of physics parameters in coupled multiphysics simulations with better computing performance. Although the FETs have been implemented in some nuclear applications, the performance of FETs using a Zernike polynomial series has never been thoroughly tested. This work performs an analysis of Zernike-based FETs on a 2D PWR pin-cell geometry and compares the simulation time and accuracy with conventional histogram tallies for reaction rate tallies needed in burnup calculations over radial rings. Figures of Merit (FOMs) are constructed for direct comparison of performance between different tally schemes and several metrics are used to determine the optimal expansion order. It is determined that Zernike-based FETs achieve comparable performance to discrete tallies, but require very high radial orders to properly capture the spatial distribution of certain reaction rates, such as U-238 absorption. A generalized functional expansion method using an arbitrary series of independent functions as basis set is then proposed and tested. To capture the self-shielding effect of the U-238 absorption rate, an exponential basis set is chosen. The results show that the exponential basis set can reduce the optimum order of expansion by half comparing with orthogonal Zernike polynomials while achieving the same accuracy. The integrated reaction rate is also demonstrated to be preserved. This work also shows that the generalized functional expansion could be a heuristic method for further investigation of continuous depletion problems.