Thesis Open Access

A neutron noise solver based on a discrete ordinates method.

Huaiqian YI


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    <subfield code="a">nuclear reactor modelling</subfield>
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    <subfield code="a">Deterministic neutron transport methods</subfield>
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    <subfield code="a">A neutron noise solver based on a discrete ordinates method.</subfield>
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    <subfield code="a">&lt;p&gt;A neutron noise transport modelling tool is presented in this thesis. The simulator allows to&lt;br&gt;
determine the static solution of a critical system and the neutron noise induced by a prescribed&lt;br&gt;
perturbation of the critical system. The simulator is based on the neutron balance equations in&lt;br&gt;
the frequency domain and for two-dimensional systems. The discrete ordinates method is used&lt;br&gt;
for the angular discretization and the diamond finite difference method for the treatment of the&lt;br&gt;
spatial variable. The energy dependence is modelled with two neutron energy groups. The&lt;br&gt;
conventional inner-outer iterative scheme is employed for solving the discretized neutron&lt;br&gt;
transport equations. For the acceleration of the iterative scheme, the diffusion synthetic&lt;br&gt;
acceleration is implemented.&lt;br&gt;
The convergence rate of the accelerated and unaccelerated versions of the simulator is studied&lt;br&gt;
for the case of a perturbed infinite homogeneous system. The theoretical behavior predicted by&lt;br&gt;
the Fourier convergence analysis agrees well with the numerical performance of the simulator.&lt;br&gt;
The diffusion synthetic acceleration decreases significantly the number of numerical iterations,&lt;br&gt;
but its convergence rate is still slow, especially for perturbations at low frequencies.&lt;br&gt;
The simulator is further tested on neutron noise problems in more realistic, heterogeneous&lt;br&gt;
systems and compared with the diffusion-based solver. The diffusion synthetic acceleration&lt;br&gt;
leads to a reduction of the computational burden by a factor of 20. In addition, the simulator&lt;br&gt;
shows results that are consistent with the diffusion-based approximation. However,&lt;br&gt;
discrepancies are found because of the local effects of the neutron noise source and the strong&lt;br&gt;
variations of material properties in the system, which are expected to be better reproduced by a&lt;br&gt;
higher-order transport method such as the one used in the new solver.&lt;/p&gt;</subfield>
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