Date of Award
Doctor of Philosophy
This research involves the development of a three-dimensional nodal code that calculates the Fourier transformed regular or adjoint neutron flux for a nuclear reactor. This numerical technique can be used in the nuclear reactor noise analysis field for identifying and locating vibrating reactor core components;The mathematical equations were developed and two types of solutions were obtained. The first solution was a modification of a three-dimensional nodal model developed to handle multigroup neutron diffusion equations. In this model, the Fourier transformed fluxes were expanded in the Legendre polynomial form. The second is an analytical procedure developed for a simple geometry and material composition. In the analytical model, the frequency-dependent flux was expanded in the eigenfunctions of the Helmholtz equation which yielded a series form solution. This solution was used to verify the validity of the nodal numerical technique;The nodal computer code was tested for 8, 64, and 216 node problems. Moreover, it was examined for frequencies inside and outside the plateau region of the zero power reactor transfer function. Frequencies considered were.05, 10, 200 and 1000 rad/s where the plateau region extends from 0.1 to 527 rad/s. The comparison between the results obtained showed that the nodal computer code can be used to calculate the frequency-dependent fluxes provided the reactor core is simulated by a large number of nodes and that the source is reduced in size so that it can represent point perturbations.
Digital Repository @ Iowa State University, http://lib.dr.iastate.edu/
Abdulghani M. Melaibari
Melaibari, Abdulghani M., "A three-dimensional nodal solution for the frequency dependent neutron diffusion equation " (1987). Retrospective Theses and Dissertations. 11707.