Linear modal analysis of out-of-phase instability in boiling water reactor cores

Abstract

An eigenvalue problem governing BWR core nuclear thermal-hydraulic modes which result in out-of-phase power oscillations is formulated. This formulation is based on the linearization approximation to nonlinear feedback terms and the very simple models for neutronics and thermal-hydraulics. The eigenvalue problem in 5 × 5 matrix formulation can be easily solved without using a computer. A series of the calculations are carried out, at a high-power and low-core-flow condition, to investigate the dependence of the eigenvalues and eigenfunctions on the void reactivity coefficient and the subcriticality of spatial neutronic modes, where the latter parameter is identical to the eigenvalue separation of the higher-harmonic neutronic mode. These results show that the threshold value of the void coefficient for initiating the unstable out-of-phase oscillation strongly depends on the subcriticality. The oscillation mode becomes more unstable with an increase in the absolute value of the negative void coefficient, whereas the mode becomes more stable, almost linearly, with increasing subcriticality. The resonant frequency of the oscillation and the phase shifts between the nuclear thermal-hydraulic variables are consistent with previous measured or calculated values.