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A Simple Formula for Local Burnup and Isotope Distributions Based on Approximately Constant Relative Reaction Rate
A simple and analytical formula is suggested to solve the problems of the local burnup and the isotope distributions. The present method considers two extreme conditions of neutrons penetrating the fuel rod. Based on these considerations, the formula is obtained to calculate the reaction rates of 235U, 238U, and 239Pu and straightforward the local burnup and the isotope distributions. Starting from an initial burnup level, the parameters of the formula are fitted to the reaction rates given by a Monte Carlo (MC) calculation. Then the present formula independently gives very similar results to the MC calculation from the starting to high burnup level but takes just a few minutes.The relative reaction rates are found to be almost independent of the radius (except (N, γ) of 238U) and the burnup, providing a solid background for the present formula. A more realistic examination is also performed when the fuel rods locate in an assembly. A combination of the present formula and the MC calculation is expected to have a nice balance between the numerical accuracy and time consumption.
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