Método del desarrollo ortogonal por zonas para la resolución de ka ecuación de difusión de neutrones
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Comisión Nacional de Energía Atómica. Argentina
Resumen
Dado un arreglo indefinido de substancia moderadora de neutrones y de material "combustible", productor de los mismos, se trata en general de resolver la ecuación de difusión, a la que satisface el flujo neutrónico en el mencionado arreglo. El método que aquí describimos, consiste en dividir la estructura o "lattice" dado, en zonas adecuadas a la geometría del arreglo. Adoptando luego un desarrollo ortogonal conveniente en cada una de esas regiones, se consigue "reducir" el problema a la solución de un sistema (infinito) de ecuaciones lineales numéricas. La forma de encarar el mencionado sistema está explicada en el texto. El método tiene la ventaja de adaptarse a diferentes casos, según se irá viendo, con relativa facilidad. La mejor manera de dar en detalle los procedimientos consistirá en examinar los diferentes problemas que iremos tratando. En el par de ejemplos que siguen, nos ocupamos de sistemas heterogéneos, en los que el combustible está concentrado en barras que van rodeadas de la substancia moderadora.
Given an indefinite arrangement of a neutron-moderating substance and a "combustible" material, which produces them, it is generally a matter of solving the diffusion equation, which is satisfied by the neutron flux in the aforementioned arrangement. The method described here consists of dividing the given structure or "lattice" into zones appropriate to the geometry of the array. By then adopting a convenient orthogonal expansion in each of these regions, the problem is "reduced" to the solution of an (infinite) system of numerical linear equations. The way to deal with the aforementioned system is explained in the text. The method has the advantage of adapting to different cases, as will be seen, with relative ease. The best way to give the procedures in detail will be to examine the different problems that we will be dealing with. In the couple of examples that follow, we deal with heterogeneous systems, in which the fuel is concentrated in rods that are surrounded by the moderating substance.
Given an indefinite arrangement of a neutron-moderating substance and a "combustible" material, which produces them, it is generally a matter of solving the diffusion equation, which is satisfied by the neutron flux in the aforementioned arrangement. The method described here consists of dividing the given structure or "lattice" into zones appropriate to the geometry of the array. By then adopting a convenient orthogonal expansion in each of these regions, the problem is "reduced" to the solution of an (infinite) system of numerical linear equations. The way to deal with the aforementioned system is explained in the text. The method has the advantage of adapting to different cases, as will be seen, with relative ease. The best way to give the procedures in detail will be to examine the different problems that we will be dealing with. In the couple of examples that follow, we deal with heterogeneous systems, in which the fuel is concentrated in rods that are surrounded by the moderating substance.