A Variational Nodal Approach to 2D/1D Pin Resolved Neutron Transport for Pressurized Water Reactors

Abstract

A two-dimensional/one-dimensional (2D/1D) variational nodal approach is presented for pressurized water reactor core calculations without fuel-moderator homogenization. A 2D/1D approximation to the within-group neutron transport equation is derived and converted to an even-parity form. The corresponding nodal functional is presented and discretized to obtain response matrix equations. Within the nodes, finite elements in the x-y plane and orthogonal functions in z are used to approximate the spatial flux distribution. On the radial interfaces, orthogonal polynomials are employed; on the axial interfaces, piecewise constants corresponding to the finite elements eliminate the interface homogenization that has been a challenge for method of characteristics (MOC)–based 2D/1D approximations. The angular discretization utilizes an even-parity integral method within the nodes, and low-order spherical harmonics (P_N) on the axial interfaces. The x-y surfaces are treated with high-order P_N combined with quasi-reflected interface conditions. The method is applied to the C5G7 benchmark problems and compared to Monte Carlo reference calculations.

Keywords:

• 2D/1D variational nodal method
• eliminating the interface homogenization

Acknowledgments

This work is supported by the China Scholarship Council, the National Natural Science Foundation of China (No. 11305123), and the U.S. Department of Energy, Office of Science, Basic Energy Sciences, under contract DE-AC02-06CH11357.