TRACE/PARCS analysis of out-of-phase power oscillations with a rotating line of symmetry

• Out-of-phase limit cycle oscillations were simulated with TRACE/PARCS.
• Flux mode amplitudes were extracted and analyzed.
• A “rotating mode” was observed, possibly arising from nonlinear effects.
• Early evolution of oscillations was highly sensitive to the initial perturbation.

A study of BWR out-of-phase oscillations has been performed with the TRACE/PARCS coupled code system. Unstable power oscillations with a time-dependent, rotating line of symmetry have been successfully simulated using input models from two different BWRs and applying simple Anticipated Transient Without Scram (ATWS) scenarios. The λ-modes of the neutron flux were calculated using an implicitly-restarted Arnoldi solver, and the time-dependent amplitudes of the fundamental, first azimuthal, and second azimuthal power modes were determined for each simulation. After progressing in an irregular, sporadic fashion, the oscillations appeared to transition into a clear “rotating mode” that was sustained indefinitely with a fixed phase shift between modes of roughly 90°. Because the phase shift did not gradually change over time, despite each mode having a different natural frequency in the linear range, the conclusion was made that a nonlinear interaction mechanism was active between the first and second subcritical azimuthal modes to maintain the constant phase shift during the limit cycle. An additional study was performed which found that a small perturbation is capable of drastically affecting the development of oscillations in a simulation when both modes (in-phase and out-of-phase) are unstable; when one of the models was modified to include a small-amplitude noise source on the first azimuthal mode, purely out-of-phase oscillations were observed, whereas the oscillations had been purely in-phase for the first 55 s when no noise signal was included. Because most ATWS event calculations involve mostly in-phase perturbations to the BWR core, it is recommended to add a small out-of-phase perturbation in simulations where both the in-phase and out-of-phase modes may be unstable.