Developments in nodal reactor analysis tools for hexagonal geometry
Fitzpatrick, William Edward
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Permalink
https://hdl.handle.net/2142/20083
Description
Title
Developments in nodal reactor analysis tools for hexagonal geometry
Author(s)
Fitzpatrick, William Edward
Issue Date
1995
Doctoral Committee Chair(s)
Ougouag, Abderrafi M.
Department of Study
Nuclear, Plasma, and Radiological Engineering
Discipline
Nuclear Engineering
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Engineering, Nuclear
Computer Science
Language
eng
Abstract
A new nodal method for the solution of multigroup multidimensional diffusion problems in hexagonal geometry is developed and implemented into the FORTRAN code HEXPEDITE. The algorithm is adapted for modern computer features including vector and concurrent computations and demonstrates high efficiency and accuracy on many 2-D and 3-D problems. Two procedures consistent with the HEXPEDITE formalism to allow the modeling of mild intranodal heterogeneities due to depletion are outlined.
Innovative solution techniques for the time-dependence of the diffusion equations are developed and are coupled to spatial nodal algorithms. In 1-D problems, an analytical solution based on linear and quadratic dependencies over discrete time intervals of the effective source are compared against finite-difference solutions. The quadratic interpolation allows much larger time steps than the other approaches on two problems.
A new method, the moment integral method, for multidimensional nodal kinetic problems is introduced. This method solves analytically the time dependence of the flux spatial moments over discrete time intervals. The moment integral method, based on an exponential fit, shows better accuracy at large time steps than a finite-difference solution on 2-D rectangular and hexagonal problems.
The completely analytical solution to the transient reactor physics equations is investigated with no approximations further than nodal diffusion theory. A formal solution is shown to be feasible and to be adaptable for a nodal algorithm in a modified form.
The telegrapher's equation describing the true wave-like changes in the neutron flux of reactor media is studied. The new semi-analytical kinetic techniques with slight modifications are applied to a multigroup 1-D model.
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