Influence of subcooled boiling on out-of-phase oscillations in boiling water reactors

In this paper, we develop a reduced order model with modal kinetics for the study of the dynamic behavior of boiling water reactors. This model includes the subcooled boiling in the lower part of the reactor channels. New additional equations have been obtained for the following dynamics magnitudes: the effective inception length for subcooled boiling, the average void fraction in the subcooled boiling region, the average void fraction in the bulk-boiling region, the mass fluxes at the boiling boundary and the channel exit, respectively, and so on. Each channel has three nodes, one of liquid, one with subcooled boiling, and one with bulk boiling. The reduced order model includes also a modal kinetics with the fundamental mode and the first subcritical one, and two channels representing both halves of the reactor core. Also, in this paper, we perform a detailed study of the way to calculate the feedback reactivity parameters. The model displays out-of-phase oscillations when enough feedback gain is provided. The feedback gain that is necessary to self-sustain these oscillations is approximately one-half the gain that is needed when the subcooled boiling node is not included.