Sensitivity and uncertainty analysis of a reduced-order model of nonlinear BWR dynamics: I. Forward sensitivity analysis

This work applies the forward sensitivity analysis method to the reduced-order Boiling Water Reactor (BWR) model originally developed by March-Leuba, Perez and Cacuci ["Universality and Aperiodic Behavior of Nuclear Reactors," Nucl. Sci. Eng. 86, 401, 1984.] to compute first-order sensitivities of the state functions (power, precursors concentration, reactivity, void fraction and fuel temperature) underlying this model. This reduced-order BWR model comprises point neutron kinetics equations coupled to thermal-hydraulics equations that describe the time evolution of the fuel temperature and coolant density in the recirculation loop. When the heat transfer from the reactor to the coolant is increased under high-power/low-flow operating conditions, this model's state functions can bifurcate, via a period-doubling cascade of bifurcations, from their steady-state values into a chaotic dynamic evolution. Numerical results for the sensitivities of the state functions with respect to a model parameter that controls the injected neutron population are presented for the following regions in phase-space: (i) the stable region; (ii) the period-one region between the 1st-order bifurcation and the 2nd-order bifurcations; (iii) the period-two region between the 2nd-order bifurcations and the 3rd-order bifurcations; (iv) the period-three region between the 3rd-order bifurcations and the 4th-order bifurcations; (v) the aperiodic/chaotic region, which arises from an infinite cascade of period-doubling bifurcations produced when the heat transfer from reactor to coolant is increased past a critical value. In particular, it is shown that the amplitudes of the oscillations of the sensitivities in the chaotic region reach massive values [+/- O(10(23))] already within 150 s after the initial perturbation. These results confirm the intuitive expectation that the BWR model is extremely unstable in the chaotic region. Ongoing work aims at performing a comprehensive sensitivity analysis of this reduced-order BWR model using the adjoint sensitivity analysis methodology, by investigating the time evolutions of the sensitivities of all state functions with respect to all model parameters, in the five regions in phase-space that are identified in this work. The sensitivities thus obtained will be used in a subsequent work to perform a comprehensive computation of the standard deviations that would be induced in the BWR model's state functions by uncertainties that affect the BWR model's imprecisely known parameter. (C) 2020 Published by Elsevier Ltd.