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Abstract

In this study, we introduce the calculation of reactivity in nuclear reactors. The proposed method uses the Euler-Maclaurin series to approximate the integral in the inverse equation of point kinetics. The approximation is done with the first three terms, the first term represents the approximation of a zero-order sum, the second term the trapezoidal rule and the third term the first Bernoulli number. These three terms improve the approximation, along with an estimate of the neutron density using the prompt jump approximation. To reduce neutron density fluctuations, a second-order Butterworth filter for the reactivity calculation was implemented, which offers the advantage of minimal delay based on only three data points. Whereas the methods reported in literature that consider noise in the neutron population, it is necessary to consider a much higher number of 225 samples, as in the case of the Savitzky-Golay filter and the first order delay low-pass filter. These filters reduce fluctuations in the calculation of reactivity but with a longer delay. To assess the accuracy of these enhancements a comparison was done for results obtained with different numerical simulations using a filter based on least squares fitting, varying the data window, the time step and fixing a polynomial of order d, using physical parameters for thermal reactors. The results of the numerical simulations indicate that the proposed method can be used to calculate the reactivity with high precision and with a high reduction of fluctuations by applying the Butterworth filter when the noise level increases.

Creative Commons License

Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.

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