Cell Homogenization Method for Pin-by-Pin Neutron Transport Calculations

Abstract

For practical reactor core applications, low-order transport approximations such as SP(3) have been shown to provide sufficient accuracy for both static and transient calculations with considerably less computational expense than the discrete ordinate or the full spherical harmonics methods. These methods have been applied in several core simulators where homogenization was performed at the level of the pin cell. One of the principal problems has been to recover the error introduced by pin cell homogenization. One of the basic approaches to treat pin cell homogenization error is pin cell discontinuity factors (CDFs) based on well-established generalized equivalence theory to generate appropriate group constants. The method is able to treat all sources of error together, allowing even a few-group diffusion solution with one mesh per cell to reproduce a higher-order reference solution. However, a CDF has to be derived separately for each space-angle approximation. An additional difficulty is that in practice the CDFs have to be derived from a lattice calculation from which only the scalar flux and current are available, and therefore recovery of the exact SP(N) angular moment is not possible. This paper focuses on the pin cell scale homogenization. It demonstrates derivation of the CDF for the SP(3) transport method with finite-difference spatial discretization with the limitation of only the scalar flux and interface current being available from the heterogeneous reference. The method is demonstrated using a sample benchmark application.