Cálculos de criticalidade usando a equação de transporte de nêutrons multigrupo unidimensional na formulação das ordenadas discretas a partir da solução analítica local

Abstract

The computational modeling for criticality calculations in nuclear reactors is currently justified, as it is directly related to the operation of power reactors, a viable energy option for mitigating problems related to the issue of global warming. In this thesis, we propose and develop two deterministic methodologies using the local analytical solution to calculate the effective multiplication factor (kef f ) and the power distribution in a nuclear reactor, considering stationary, one-dimensional cartesian geometry problems, using the linearized equation of Boltzmann for the transport of neutrons, in the formulation of multigroup discrete ordinates (SN ). The proposed methodologies, called ASNM, c.f., Analytical Spectral-Nodal Method and ASNM-SI, c.f., Analytical Spectral-Nodal Method - Source Iteration, belong to the class of spectral-nodal methods (coarse mesh) and were implemented to solve calculation problems of criticality. Numerical results for four model problems are presented, considering different types of boundary conditions (vacuum and reflective) and different numbers of energy groups. The numerical results obtained when several spatial grids and different quadrature orders were used were the same or similar in both methodologies. The numerical results were compared with two reference methods, the traditional fine-mesh method DD, c.f., Diamond Difference (in all model problems) and the spectral-nodal method (coarse mesh) SD-SGF, c.f., spectral Diamond- spectral Green’s function, used in the first three model problems presented in the thesis. The numerical algorithms were implemented in the C++ language, using the LAPACK, SCA LAPACK, AlgLib numerical calculus libraries. Parallels of the proposed methodologies were also implemented using the MPI standard, c.f., Message Passing Interface for its use in clusters.