# Quadrature formulas for integral equations of kinetics and for digital reactimeters

6/21/2017 2017 - #02 Modelling processes at nuclear facilities

https://doi.org/10.26583/npe.2017.2.09

### UDC: 621.039.515:621.039.516.2:621.039.514.4

The aim of work is the derivation of quadrature formulas for a kinetic equations nuclear reactor in the form of Volterra integral equations of the second kind and for equation of a reactimeter in the form of integral convolution, the core of which is a function of decay of the delayed neutron precursors (DNP) in the nongroup 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 reduces to the calculation of the delayed neutrons integral. This eliminates the source of discrepancy calculated and experimental evaluations of reactivity due to the difference in computational algorithms direct and inverse problems. The paper describes a general scheme to convert different transport equation approximations to describe the contribution of delayed neutrons by a integral convolution without using dynamics of the DNP concentration. This conversion reduces the dimension of the model, simplifies the software implementation, eliminates the stiffness problem of differential equations of the kinetics, provides stability of calculations. The dimension of the model is preserved in the case of several fissile nuclides. The integral form of the equations admits in quadrature formulas the use the samples of experimental function of the decay, which can be identified in the operating conditions of a nuclear reactor and stored by pointwise in the non-group form – without expansions in sum of the exponents. This eliminates the need to address the nonlinear problem of identification of the group parameters of delayed neutrons and increases the adequacy of modeling. In work is obtained a series of quadrature formulas for the calculation of the delayed neutrons integral and describes the corresponding algorithms of digital reactimeter and the numerical simulation of the reactor kinetics.

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dynamics of nuclear reactor point kinetics reactivity reactimeter integral equations quadrature formulas