An advanced nodal discretization for the quasi-diffusion low-order equations

• Main Author: Nes, Razvan
• Other Authors: Palmer, Todd S.
• Language: en_US
• Published: 2012
• Subjects: Neutron flux > Mathematical models; Light water reactors > Mathematical models; Neutron transport theory
• Online Access: http://hdl.handle.net/1957/30335

The subject of this thesis is the development of a nodal discretization of the low-order quasi-diffusion (QDLO) equations for global reactor core calculations. The advantage of quasi-diffusion (QD) is that it is able to capture transport effects at the surface between unlike fuel assemblies better than the diffusion approximation. We discretize QDLO equations with the advanced nodal methodology described by Palmtag (Pal 1997) for diffusion. The fast and thermal neutron fluxes are presented as 2-D, non-separable expansions of polynomial and hyperbolic functions. The fast flux expansion consists of polynomial functions, while the thermal flux is expanded in a combination of polynomial and hyperbolic functions. The advantage of using hyperbolic functions in the thermal flux expansion lies in the accuracy with which hyperbolic functions can represent the large gradients at the interface between unlike fuel assemblies. The hyperbolic expansion functions proposed in (Pal 1997) are the analytic solutions of the zero-source diffusion equation for the thermal flux. The specific form of the QDLO equations requires the derivation of new hyperbolic basis functions which are different from those proposed for the diffusion equation. We have developed a discretization of the QDLO equations with node-averaged cross-sections and Eddington tensor components, solving the 2-D equations using the weighted residual method (Ame 1992). These node-averaged data are assumed known from single assembly transport calculations. We wrote a code in "Mathematica" that solves k-eigenvalue problems and calculates neutron fluxes in 2-D Cartesian coordinates. Numerical test problems show that the model proposed here can reproduce the results of both the simple diffusion problems presented in (Pal 1997) and those with analytic solutions. While the QDLO calculations performed on one-node, zero-current, boundary condition diffusion problems and two-node, zero-current boundary condition problems with UO₂-UO₂ assemblies are in excellent agreement with the benchmark and analytic solutions, UO₂-MOX configurations show more important discrepancies that are due to the single-assembly homogenized cross-sections used in the calculations. The results of the multiple-node problems show similar discrepancies in power distribution with the results reported in (Pal 1997). Multiple-node k-eigenvalue problems exhibit larger discrepancies, but these can be diminished by using adjusted diffusion coefficients (Pal 1997). The results of several "transport" problems demonstrate the influence of Eddington functionals on homogenized flux, power distribution, and multiplication factor k. === Graduation date: 2003