Quadrature formulas for integral equations of kinetics and digital reactimeters

Abstract

The aim of this work is to derive quadrature formulas for nuclear reactor kinetic equations in the form of Volterra integral equations of the second kind and reactimeter equations in the form of integral convolution, the kernel of which is a decay function of delayed neutron precursors (DNP) in the non-group form. The expediency of the transition to integral equations is caused by the unification of the direct (calculation of power dynamics) and the reverse (calculation of current reactivity) tasks of reactor kinetics. As a result, the solution is reduced to the calculation of the delayed neutrons integral (DNI). This eliminates the source of computational-experimental discrepancies in estimations of reactivity, which is due to the difference in computational algorithms of direct and inverse problems. The paper describes a general scheme for converting different transport equation approximations to describe the contribution of delayed neutrons by means of an integral convolution without using dynamic equations of the DNP concentration. This conversion reduces the model dimension, simplifies the software implementation, eliminates the stiffness problem of differential kinetic equations and provides the stability of calculations. The model dimension is preserved in the case of several fissile nuclides. The integral form of the equations makes it possible to use the experimental decay function in quadrature formulas, which can be identified in the operating conditions of a nuclear reactor and stored pointwise in a nongroup form without decomposition into the sum of exponentials. This eliminates the need to solve the non-linear problem of identifying group parameters of delayed neutrons and increases the adequacy of modeling. A series of quadrature formulas for the calculation of the DNI are obtained and the corresponding algorithms of a digital reactimeter and numerical simulation of the reactor kinetics are described. Copyright © 2017, National Research Nuclear University MEPhI (Moscow Engineering Physics Institute). Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license. (http://creativecommons.org/licenses/by-nc-nd/4.0/)