Spelling suggestions: "subject:"neutron flux -- amathematical models"" "subject:"neutron flux -- dmathematical models""
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Neutron transport benchmarks for binary stochastic multiplying media : planar geometry, two energy groupsDavis, Ian M. (Ian Mack) 10 March 2005 (has links)
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
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An advanced nodal discretization for the quasi-diffusion low-order equationsNes, Razvan 17 May 2002 (has links)
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
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Application of response matrix methods to PWR analysisParsons, Donald Kent January 1982 (has links)
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.
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