Interpretation of in-phase and out-of-phase BWR oscillations using an extended reduced order model and semi-analytical bifurcation analysis

An extended reduced order model is presented and applied to analyze global and regional oscillations in BWRs. Stability and semi-analytical bifurcation analyses are performed using this model in conjunction with the bifurcation code BIFDD to determine the stability limits for both in-phase and out-of-phase oscillation modes and the nature of Poincaré–Andronov–Hopf bifurcation. The results obtained show that both sub- and supercritical PAH bifurcations are encountered in different regions of the parameter space. An in-depth investigation of the properties of the elements of the eigenvectors associated with these two modes of oscillation is carried out. Results show that these eigenvectors provide information as regards the corresponding oscillation mode (in-phase or out-of-phase) without solving the set of system ODEs. The analysis clearly brings out the fact that in-phase and out-of-phase oscillations are whole-system mechanisms. A clear distinction is thereby made between these oscillation modes, on the one hand, and the fundamental and first azimuthal neutronics modes on the other hand.