Nuclear Science and Engineering / Volume 190 / Number 1 / April 2018 / Pages 73-92
Technical Paper / dx.doi.org/10.1080/00295639.2017.1407593
The nonlinear stability analysis of a boiling water reactor (BWR) is presented using a nuclear-coupled thermal-hydraulic reduced-order model. Unlike the existing studies, the effect of reactivity feedbacks (void reactivity feedback and temperature feedback) on nonlinear stability characteristics is presented in this work. The analytical model comprises point-kinetics equations with one group of delayed neutrons and fuel heat transfer having coupling with single-phase and two-phase one-dimensional reduced homogeneous thermal hydraulics wherein the two intrinsic reactivity feedbacks, namely, Doppler and void, provide the coupling feature. The primary objective of the present work is to delineate the stability and bifurcation characteristics of BWRs, and this is achieved in two levels. The first level is linear stability analysis wherein the linear stability boundaries are shown in parameter space constituted by two intrinsic reactivity feedbacks and in the subcooling versus phase change number plane as well. In the second level, we discuss the nonlinear characteristics, and the existence of subcritical and supercritical Hopf bifurcations is ascertained by a method of multiple time scales. Numerical simulations are performed to verify the resultant limit cycle behavior (arising from Hopf bifurcation) followed by the turning point bifurcations, and period-doubling bifurcation leading to chaos. Further, a parametric study is performed to show the effect of variation of various nondimensional parameters on the system dynamics and is depicted with the help of a criticality curve that delineates the two Hopf bifurcation regimes in parameter spaces formed by dimensionless reactivities (Doppler and void) and dimensionless numbers (subcooling and phase change). The study implies that the larger values of reactor power, phase change number, and subcooling number favor the supercritical Hopf bifurcation and hence assure globally safe reactor operation.