Source projection analytic nodal $S_N$ method for analysis of non-rectangular assembly cores

Abstract

The transport of neutrons through a medium of a physical system is commonly described by the mathematical description called transport theory. In large nuclear systems, fine-mesh technique such as the finite-difference method becomes extraordinarily expensive in solving the integral or integro-differential form of the transport equation. Therefore, in the last few decades several nodal (coarse-mesh) methods have been developed and implemented for the solutions of the neutron transport problems. The objective of this thesis is to develop a hexagonal nodal transport method for analysis of non-rectangular assembly cores such as the fast breeder reactor core. For this purpose, the author developed a new nodal $S_N$ method called the Source Projection Analytic Nodal Discrete Ordinates Method (SPANDOM) which has unique features as the following. SPANDOM does not invoke the transverse integration procedure but instead directly solves the two-dimensional discrete ordinates equation after the source term is projected and represented in high-order polynomials and/or exponential functions. The solution of the discrete ordinates transport equation is decomposed into its particular and homogeneous parts. They are then analytically solved with boundary condition. With regard to the unit node for source representation in SPANDOM, three approaches have been developed for the hexagonal geometry: Triangle approach (SPANDOM-TA), Half-Hexagon approach (SPANDOM-HH), and Full-Hexagon approach (SPANDOM-FH). In order to validate the accuracy and applicability of SPANDOM, the three approaches have been tested on two fast reactor benchmark problems and the numerical results are compared with those of the TWOHEX code. The results of comparison indicate that the present SPANDOM predicts accurately not only the effective multiplication factor but also the flux distributions in non-rectangular cores with hexagonal assemblies, even in the region where flux varies very rapidly. Th...