Contributions to solve the multi-group neutron transport equation with different angular approaches
- Autores: Sergio Morato Rafet
- Directores de la Tesis: Rafael Miró Herrero (dir. tes.), Álvaro Bernal García (dir. tes.)
- Lectura: En la Universitat Politècnica de València ( España ) en 2020
- Idioma: español
- Tribunal Calificador de la Tesis: Guillermo Iván Maldonado (presid.), Nuria García Herranz (secret.), Rafael Macian Juan (voc.)
- Programa de doctorado: Programa de Doctorado en Ingeniería y Producción Industrial por la Universitat Politècnica de València
- Materias:
- Enlaces
- Tesis en acceso abierto en: RiuNet
- Resumen
The most accurate way to know the movement of the neutrons through matter is achieved by solving the Neutron Transport Equation. Three different approaches to solve this equation have been investigated in this thesis: Discrete Ordinates Neutron Transport Equation, Neutron Diffusion Equation and Simplified Spherical Harmonics Equations.
In order to solve the equations, different schemes of the Finite Differences Method were studied. The solution of these equations describes the population of neutrons and the occurred reactions inside a nuclear system. These variables are related with the flux and power, fundamental parameters for the Nuclear Safety Analysis.
The thesis introduces the definition of the mentioned equations. In particular, they are detailed for the steady state case. The Modal Method is proposed as a solution to the eigenvalue problems determined by the equations.
First, several algorithms for the solution of the steady state of the Neutron Transport Equation with the Discrete Ordinates Method for the angular discretization and Finite Difference Method for spatial discretization are developed. A formulation able to solve eigenvalue problems for any number of energy groups, with scattering and anisotropy has been developed. Several quadratures used by this method for the angular discretization have been studied and implemented for any order of approach of the discrete ordinates. Furthermore, an adapted formulation has been developed as a solution of the source problem for the Neutron Transport Equation.
Next, an algorithm is carried out that allows to solve the Neutron Diffusion Equation with two variants of the Finite Difference Method, one with cell centered scheme and another edge entered. The Modal method is also used for calculating any number of eigenvalues for several energy groups and upscattering.
Both Finite Difference schemes mentioned before are also implemented to solve the Simplified Spherical Harmonics Equations. Moreover, an analysis of different approaches of the boundary conditions is performed.
Finally, calculations of the multiplication factor, subcritical modes, neutron flux and the power for different nuclear reactors were carried out. These variables result essential in Nuclear Safety Analysis. In addition, several sensitivity studies of parameters like mesh size, quadrature order or quadrature type were performed.
