Averaging the neutron diffusion equation |
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| Authors: | R. Vázquez-Rodríguez G. Espinosa-Paredes J.B. Morales-Sandoval A. Vázquez-Rodríguez E.-G. Espinosa-Martinez |
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| Affiliation: | 1. Área de Ingeniería en Recursos Energéticos, Universidad Autónoma, Metropolitana-Iztapalapa, Av. San Rafael Atlixco 186 Col. Vicentina, México, 09340 D.F., Mexico;2. Laboratorio de Análisis en Ingeniería de Reactores Nucleares, Universidad Nacional Autónoma de México, Paseo Cuauhnáhuac 8532, 62550 Jiutepec, Mor., Mexico;3. Retorno Québec 6, Col. Burgos de Cuernavaca 62580, Temixco, Mor., Mexico;1. School of Nuclear Science and Engineering, Shanghai Jiao Tong University, 800 Dong Chuan Road, Shanghai 200240, China;2. Shanghai NuStar Nuclear Power Technology Co., Ltd., Shanghai 200235, China;1. División de Ciencias Básica e Ingeniería, Universidad Autónoma Metropolitana-Iztapalapa, Av. San Rafael Atlixco 186, Col. Vicentina, México D.F., 09340, Mexico;2. División de Ciencias y Biológicas de la Salud, Universidad Autónoma Metropolitana-Iztapalapa, Av. San Rafael Atlixco 186, Col. Vicentina, México D.F., 09340, Mexico;3. Department of Electronics Engineering, Ramrao Adik Institute of Technology, Nerul, Navi Mumbai, 400 706, India;4. IDP in Systems and Control Engineering, Indian Institute of Technology Bombay, Mumbai, 400 076, India;1. Instituto Nacional de Investigaciones Nucleares, Carr. Mexico-Toluca s/n, La Marquesa, C.P. 52750 Ocoyoacac, Edo. de México, Mexico;2. Escuela Superior de Física y Matemáticas, Instituto Politécnico Nacional, San Pedro Zacatenco, C.P. 07738 Cd. de México, Mexico |
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| Abstract: | This paper presents a general theoretical analysis of the neutron motion problem in a nuclear reactor, where large variations on neutron cross-sections normally preclude the use of the classical neutron diffusion equation. A volume-averaged neutron diffusion equation (VANDE) is derived which includes correction terms to diffusion and nuclear reaction effects. A method is presented to determine closure-relationships for the VANDE (e.g., effective diffusivity). In order to describe the distribution of neutrons in a highly heterogeneous configuration, it was necessary to extend the classical neutron diffusion equation. Thus, the averaged diffusion equation includes two correction factors: the first correction is related with the absorption process of the neutron and the second correction is a contribution to the neutron diffusion, both parameters are related to neutron effects on the interface of a heterogeneous configuration. As an example of the VANDE, the plane source in an infinite medium was considered to study the effects of the correction factors on the neutron flux, and the results were compared with classic solution. |
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