Stability analysis of BWR using the bifurcation theory

This paper presents a new approach using the bifurcation theory for the stability analysis of BWR. In this approach, the dependencies of the equilibrium states on the parameters that have a large influence on the stability are investigated topologically over a wide range of phase space. The stability information can be derived from the analysis of the bifurcation phenomena on equilibrium states. This investigation enables one to obtain qualitative and global information on the stability of a nonlinear system. The new approach was applied to the analysis of BWR instability phenomena accompanied with an in-phase power oscillation. The analysis for the dependencies of the stability boundary on the various parameters revealed that the loss of linear stability took place at the Hopf bifurcation points and the channel hydrodynamics heavily took part in the BWR instability phenomena. The analysis for the Hopf bifurcation proved that the bifurcated periodic state was orbitally unstable in the vicinity of the Hopf bifurcation point. This fact led to the conclusion that the power oscillation observed in the BWR instability was not a limit cycle oscillation in a rigid sense, but a periodic motion gradually departing away from the orbitally unstable orbit