On-line reactivity calculation using Lagrange method

Abstract

In this paper, a novel multi-step method is proposed for solving the inverse point kinetics problem using Lagrange polynomial method. By use of this approach, the need for nuclear power history or the Laplace transform is vanished. Furthermore, the accuracy of the method is of order hn for the (n+1)-point formula, where h is the computational time-step.The three- and five-point formulas of the Lagrange method are used for on-line reactivity calculations and results are benchmarked against reference solutions for different nuclear power forms. Moreover, results for different computational time-steps are compared in each case.The results show the accuracy of the proposed method in all benchmarking cases. For slow transients (large reactor periods), it is shown that time-steps of up to 1s lead to highly reliable reactivity calculations. However, the optimal time-step in almost all cases is shown to be 0.1s. The main advantage of the proposed approach, in contrast with previous numerical methods, is its stability and convergence in large time-step calculations.The proposed method can be used as real time reactivity meter in all nuclear reactors without limitation of nuclear power form.