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Development of a Numerical Tool for Estimating the Neutron Noise in Nuclear Reactors

Licentiate thesis, 2009

The neutron noise, i.e. the time-variations of the neutron flux around its mean
value, can be used for obtaining important safety parameters in a nuclear reactor,
e.g. the decay ratio for a boiling water reactor and the moderator temperature coefficient
for a pressurized water reactor. The main benefit of using the neutron noise
is that it can be taken from the existing detectors and there is therefore no need for
perturbing reactor operation. It would thus be advantageous to be able to calculate
the neutron noise with a relatively simple model with a relatively small computational
effort, a work initiated earlier at the Department of Nuclear Engineering,
Chalmers University of Technology.
The objectives of this report are thus to validate some of the assumptions in
the previously developed model and to evaluate various ways of improving it. A
comparison is thus conducted between P1 and diffusion theories with two energy
groups for a 1-dimensional 2-region reactor. The previous model used the Finite
Difference Method, a method which is simple and easy to implement for spatial
discretization of the equations. The drawback is that the accuracy is low unless
the size of the nodes of the reactor model is small. To enhance the neutronics while
keeping the size of the nodes in the range of 15-20 cm, theAnalytical Nodal Method
was implemented for the calculation of the neutron noise.
The results fromthis study are that there is no need in practical situations for using
higher order theory for neutron noise calculations since diffusion theory gives
results that are accurate enough. The implemented Analytical Nodal Method also
shows high agreement with the analytically calculated neutron noise.

neutron noise

P1 theory

Analytical
Green’s function

Analytical Nodal Method

P1 theory

Finite Difference Method

Green’s function

diffusion theory

diffusion theory