Resolving subgrid heterogeneity using the subray method of characteristics

Planar synthesis methods are a popular class of methods for direct whole-core transport in reactor analysis. These methods provide accurate, high fidelity solutions to the transport equation without the computational expense of full core Monte Carlo or 3D transport. One limitation with these methods lies in the assumption that each 2D plane being solved is axially homogeneous. When this assumption is violated, volume homogenization of cross sections must be performed up front to allow the 2D transport calculations to take place. This homogenization process does not correctly preserve reaction rates, introducing errors that are potentially unacceptable into the solution. This work presents a new subgrid method that can be used to resolve these axial heterogeneities. The new method is a variation on the well-known method of characteristics (MOC) called subray MOC. In this method, axial heterogeneity is treated explicitly by the 2D MOC calculations by splitting and recombining rays during each sweep, capturing the 3D effects of the axial heterogeneity without substantial increases in computational expense. First, brief descriptions of the 2D/1D method, which is a type of planar synthesis method, and traditional MOC are presented. Next, the need for subgrid methods in 2D/1D is motivated, followed by a detailed description of subray MOC. Finally, results are obtained for the C5G7 benchmark problems using the new method. These results show that subray MOC is effective in reducing the errors caused by partially inserted rods. In the worst case, the maximum 3D pin power error is reduced from about 55% to less than 2%, and the k_efferror in the same case is reduced from -1730 pcm to -46 pcm. The method is also shown to improve on another recently developed subgrid method.