A 2-D/1-D Transverse Leakage Approximation Based on Azimuthal, Fourier Moments

The MPACT code being developed collaboratively by Oak Ridge National Laboratory and the University of Michigan is the primary deterministic neutron transport solver within the Virtual Environment for Reactor Applications Core Simulator (VERA-CS). In MPACT, the two-dimensional (2-D)/one-dimensional (1-D) scheme is the most commonly used method for solving neutron transport�based three-dimensional nuclear reactor core physics problems. Several axial solvers in this scheme assume isotropic transverse leakages, but work with the axial S_N solver has extended these leakages to include both polar and azimuthal dependence. However, explicit angular representation can be burdensome for run-time and memory requirements. The work here alleviates this burden by assuming that the azimuthal dependence of the angular flux and transverse leakages are represented by a Fourier series expansion. At the heart of this is a new axial SN solver that takes in a Fourier expanded radial transverse leakage and generates the angular fluxes used to construct the axial transverse leakages used in the 2-D�Method of Characteristics calculations.

These new capabilities are demonstrated for the rodded Takeda light water reactor benchmark problem and the extended C5G7 benchmark suite. Results with heterogeneous pins, as in the C5G7 benchmark, indicate that cancelation of error between the angular and spatial representation of the transverse leakages may be a factor in the results obtained. To test this, an alternative C5G7 problem has been formulated using homogenized pin cells to reduce the errors introduced by assuming that the axial transverse leakage is spatially flat. In both the Takeda and C5G7 problems with homogeneous pins, excellent agreement is observed at a fraction of the run time and with notable reductions in memory footprint.