Benchmark calculations are performed for neutron transport in a two material (binary) stochastic multiplying medium. Spatial, angular, and energy dependence are included. The problem considered is based on a fuel assembly of a common pressurized water nuclear reactor. The mean chord length through the assembly is determined and used as the planar geometry system length. According to assumed or calculated material distributions, this system length is populated with alternating fuel and moderator segments of random size. Neutron flux distributions are numerically computed using a discretized form of the Boltzmann transport equation employing diffusion synthetic acceleration. Average quantities (group fluxes and k-eigenvalue) and variances are calculated from an ensemble of realizations of the mixing statistics. The effects of varying two parameters in the fuel, two different boundary conditions, and three different sets of mixing statistics are assessed. A probability distribution function (PDF) of the k-eigenvalue is generated and compared with previous research. Atomic mix solutions are compared with these benchmark ensemble average flux and k-eigenvalue solutions. Mixing statistics with large standard deviations give the most widely varying ensemble solutions of the flux and k-eigenvalue. The shape of the k-eigenvalue PDF qualitatively agrees with previous work. Its overall shape is independent of variations in fuel cross-sections for the problems considered, but its width is impacted by these variations. Statistical distributions with smaller standard deviations alter the shape of this PDF toward a normal distribution. The atomic mix approximation yields large over-predictions of the ensemble average k-eigenvalue and under-predictions of the flux. Qualitatively correct flux shapes are obtained, however. These benchmark calculations indicate that a model which includes higher statistical moments of the mixing statistics is needed for accurate predictions of binary stochastic media k-eigenvalue problems. This is consistent with previous findings. / Graduation date: 2005

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

Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Nuclear Engineering, 1982. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND SCIENCE. / Includes bibliographical references. / by Donald Kent Parsons. / M.S.