CRITICALITY CALCULATION OF A HOMOGENOUS CYLINDRICAL NUCLEAR REACTOR CORE USING FOUR-GROUP DIFFUSION EQUATIONS

Year 2018, Volume: 2 Issue: 3, 130 - 138, 01.09.2018

Babatunde Michael Ojo Musibau Keulere Fasasi Ayodeji Olalekan Salau , Stephen Friday Olukotun Mathew Ademola Jayeola

https://doi.org/10.31127/tuje.411549

Cited By: 1

Abstract

In this study, we present a general equation for Finite Difference Method Multi-group Diffusion (FDMMD) equations of a cylindrical nuclear reactor core. In addition, we developed an algorithm which we called TUNTOB for solving the FDMMD equations, determined the fluxes at each of the mesh points and calculated the criticality of the four energy group. This was with a view to using the four-group diffusion equations to estimate the criticality of a cylindrical reactor core that will be accurate and locally accessible for nuclear reactor design in developing countries. The multi-group diffusion equations were solved numerically by discretization using the Finite Difference Method (FDM) to obtain a general equation for a cylindrical reactor core. The fluxes at each mesh point and the criticality of the four energy group were then determined. From the results obtained, we observed that an increment in iteration led to an increase in the effective multiplication factor (𝒌𝒆𝒇𝒇) with a corresponding increase in the computation time. A maximum effective multiplication factor was reached when the number of iteration was 1000 and above. Having established the optimal number of iterations, the effects of the mesh sizes on the computation examined revealed that the values of 𝒌𝒆𝒇𝒇 increases as the mesh sizes becomes smaller until an optimal mesh size of 1 x 1 cm² was reached and further decrease in mesh sizes gave no further improvement in the value of 𝒌𝒆𝒇𝒇. The Study concluded that the accuracy in the values of 𝒌𝒆𝒇𝒇 and the smoothness of the neutron distribution curves in 3-D representations depend on the number of mesh points.

Keywords

four-group diffusion equation, effective multiplication factor, mesh size, reactor, Criticality calculation

References

• Atomic Energy Control Board of Canada, Fundamental of Power Reactors. Canada: Atomic Energy Control Board of Canada (AECBC), pp. 1-3, 1993. Available [online]: http://www.thecanadianencyclopedia.ca/en/article/atomic-energy-control-board/
• A. Arzhanov, Analytical Models of Critical Reactor in Simple Geometries. Royal Institute of Technology, Department of Physics. Stockholm, Sweden: KTH Engineering Sciences, pp. 1-33, 2010.
• B. Ganapol, Verification of the CENTRM Module for Adaptation of the SCALE Code to NGNP Prismatic and PBR Core Designs, Univeristy of Arizona. Arizona: Reactor Concepts RD&D, 2014.
• D. B. Ganapol, The Analytical Solution to the Multigroup Diffusion Equation in One - Dimensional Plane, Cylindrical and Spherical Geometries, Joint International Tropical on Mathematics and Computation and Supercomputing in Nuclear Application, 2007.
• J. D. Burnham, Reactor Theory - The Steady State, Nuclear Training Course, 1967.
• J. J. Duderstadt and J. L. Hamilton, Nuclear Reactor Analysis. Michigan: John Wiley & Sons, Inc, 672p, 1976.
• J. T. Urbatsch, Iterative Acceleration Methods for Monte Carlo and Deterministic Criticality. California: Los Alamos National Laboratory, pp. 1-174, 1995. Available [online]: https://www.osti.gov/scitech/servlets/purl/212566
• J. Kiusalaas, Numerical Methods in Engineering with Matlab, New York: Cambridge University Press, pp. 1-435, 2005.
• M. A. Jayeola, M. K. Fasasi, A. A. Amosun, A. O. Salau, B. M. Ojo (2018), Numerical Computation of Fission-Product Poisoning Build-up and Burnup Rate in a Finite Cylindrical Nuclear Reactor Core, Bilge International Journal of Science and Technology Research, Vol. 2(1), pp. 17-30.
• M. S. Stacey, Nuclear Reactor Physics. Atlanta: Wiley-Vch Verlag Gmbh & Co. KGaA, Weinheim, 735p., 2007.
• R. J. Larmash and J. A. Baratta, Introduction to Nuclear Engineering (3rd edition), New Jersey, 420p., 2001.
• T. Tanbay and O. Bilge, Numerical Solution of the Multigroup Neutron Diffusion Equation by the Meshless RBF Collocation Method, Mathematical and Computational Applications, Vol. 18, pp. 399-407, 2013.
• W. H. Harman, Modelling Pressurized Water Reactor Kinetics, Ohio, Wright-Patterson Air Force Base, 2001.