dc.description.abstract |
The instantaneous neutron’s density in a reactor core is influenced by several
factors. Some of them include the reactor material’s characteristics and the reactor
configuration geometry properties. The role of the former has been well explored
and understood while the latter continues to arouse interest in research and
applications despite being poorly understood for some configuration types. In
particular, spheroid configuration exhibits relatively higher robustness compared
to other. However, the behavior of time dependent neutron flux at varying axis
ratios and how the latter affects neutron leakage rates has not been well explored
for this type of configuration. Therefore, this study is aimed at establishing how
the axis ratio determines the behavior of neutron flux and neutron leakage rates.
Specifically; modeling and determining the behavior of time dependent neutron
diffusion flux in a spheroid reactor core at varying axis ratios, formulating the
relationship between the axis ratio and neutron leakage rates and elaborating the
behavior of neutron leakage rates for both spheroids at axis ratios equal, smaller
and larger than unity. In order to carry out this, Fick’s law of diffusion was
modified into a Jacobi elliptic theta function to describe the desired time
dependent neutron diffusion problem in spheroid coordinates system. The quasi-
radial component was adapted to represent the axis ratio and thereafter appropriate
boundary conditions were imposed. Secondly, a relationship between neutron
leakage rate and the axis ratio of spheroids was formulated using geometric
buckling and neutrons thermal life time equations, and the results were evaluated
for axis ratios equal, smaller and larger than unity with software used to solve all
the formulated equations. It was found that neutrons diffuse outwards from the
core towards the boundaries of the spheroid exhibiting the characteristics of Jacobi
elliptic theta curves of the third kind. Various configurations of diffusion
configurations were obtained that included ternary surfaces, continuous and
discontinuous surfaces of various characteristics as the value of ‘n’ was varied. In
addition, neutrons diffusion behavior along the quasi-angular component and the
time component was found to be largely similar. In the investigation of neutron
leakage rate versus the axis ratio, both configurations (with the same volume and
same neutron leakage constant (k)) exhibited similar profile, although the neutron
leakage rate for prolate was lower compared to that of oblate at axis ratios smaller
than unity. In contrast, at axis ratios larger than unity, it was found that the
neutrons leakage rate for prolate became greater than that of an oblate of the same
volume. The results further showed that, at axis ratio larger than unity, the neutron
leakage rate was mildly affected by the axis ratio of the spheroid. Finally, the
values for neutron leakage rates for both prolate and oblate spheroids converged
when the axis ratio was unity, for instance, the neutron leakage rates for both types
of spheroids was 2.5 neutrons/square unit for neutron leakage constant of k = 200.
The findings of this study could be utilized in the design of superior reactors with
enhanced safety that can mitigate against nuclear accidents by varying core axis
ratios in order to alter reactor criticality conditions. Further research needs to be
conducted on multigroup neutron diffusion for a similar problem and determining
the flux behavior for each type of spheroid separately |
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