BWR stability and bifurcation analysis using a novel reduced order model and the system code RAMONA

Boiling water reactor (BWR) stability analysis is usually carried out using large system codes. However, because of the large computational efforts required, such codes cannot in practice be employed for the detailed investigation of the complete manifold of solutions of the nonlinear differential equations describing the BWR system. In this context, reduced order models, containing a minimum number of system equations describing the most important physical phenomena, become necessary to provide deeper insight into the physical mechanisms underlying the different instability phenomena observed in BWRs, e.g. in-phase and out-of-phase power oscillations. A novel analytical, reduced order model has been currently developed to simulate the different types of instabilities encountered in heated channels and BWRs, viz. density wave oscillations (DWOs), as well as in-phase and out-of-phase oscillations in the reactor core. The complete model comprises three main parts: spatial lambda- mode neutron kinetics with the fundamental and first azimuthal modes, fuel heat conduction dynamics, and core thermal- hydraulics based on a drift flux model representation of the two-phase flow. Stability and semi-analytical bifurcation analysis is carried out for a purely thermal-hydraulic system (heated channel), as well as for a complete BWR (represented via two-channel nuclear-coupled thermal-hydraulics), using the current reduced order model in conjunction with the bifurcation code BIFDD. The impact of the drift flux parameters on the stability boundary (SB) and nature of bifurcation has thereby been investigated. Results show that both sub- and supercritical Hopf bifurcations are encountered along the stability boundary. Using a drift flux model instead of a homogeneous equilibrium model for the two-phase flow is found to have significant effects on the SB, as well as on the nature of Hopf bifurcation. For independent confirmation of the results of the semi- analytical bifurcation analyses, as well as to evaluate the system behaviour in regions away from the stability boundary, numerical integration has been carried out of the set of ordinary differential equations (ODEs) involved in each case. With each of the two channels of the currently developed BWR reduced order model representing half of the reactor core, it has been possible to apply it to the investigatio n of out-of-phase instability phenomena as well. First, the stability limits for in-phase and out-of-phase BWR oscillation modes for a generic case are determined in parameter space. An in-depth investigation is then performed of the properties of the elements of the eigenvectors associated with these two oscillation modes. Results show that analysing the properties of the eigenvectors can provide full information as regards the corresponding oscillation mode (in-phase or out-of-phase) without solving the set of system ODEs. In addition, such analysis conclusively shows that in-phase and out-of-phase oscil