Analysis of Infinite Domain Criticality Zones in Finite Reactors (Uniform Power, Minimum Fuel Density, Exact Solutions, Poles of Bromwich Integral, Reduction of Pde's)
Salimi, Behzad
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https://hdl.handle.net/2142/70906
Description
Title
Analysis of Infinite Domain Criticality Zones in Finite Reactors (Uniform Power, Minimum Fuel Density, Exact Solutions, Poles of Bromwich Integral, Reduction of Pde's)
Author(s)
Salimi, Behzad
Issue Date
1986
Department of Study
Nuclear Engineering
Discipline
Nuclear Engineering
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Engineering, Nuclear
Abstract
A reactor that is infinitely large has two ideal properties: (1) The fission rate density and, hence, the power are uniform throughout, and (2) the fuel density needed for criticality is minimum. A finite reactor loaded in this way would be subcritical and would have to contain additional fuel to compensate for neutron leakage to sustain criticality.
The performance of two reactor models is analyzed on the basis of the multi-group diffusion approximation. Both models comprise a primary inner core zone which would be critical if it were infinite in extent.
In the first model, the primary core zone is surrounded by a secondary core which is loaded to achieve a specific power density (i.e., fission rate density). The exact solutions of the multi-group diffusion equations are obtained for up to four energy groups.
In the second model, the primary core zone contains a "thin" spherical fission plate. The exact solutions of the one- and two-group diffusion equations are obtained.
A numerical example for each model is worked out to show the distribution of flux, fuel loading, and power, for the one- and two-group cases. The ratio of the peak-to-average power is calculated as a measure of the relative performance of the two models. The comparison of the power peak-to-average ratios indicates that the first model (primary inner core with outer specified power zone) is superior. Moreover, this model has a nearly ideal value for this ratio, requires no transcendental equations to be solved for criticality, and can be analyzed analytically in few group models.
Finally, the problem of uniform power in a two-dimensional assembly is analyzed. Formal analytic solutions are obtained, with one- and two-group equations, in a semi-infinite slab, and a finite cylinder.
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