On out-of-phase higher mode oscillations with rotation and oscillation of symmetry line using an advanced integral stability methodology

• Advanced integral stability analysis methodology has been developed.
• Out-of-phase mode with rotation and oscillation of symmetry line has been simulated.
• Higher order out-of-phase modes have been obtained.
• Limit cycle oscillations are associated to the occurrence of supercritical Hop bifurcation.

A new stability analysis methodology for the Swiss BWRs is being established at the Paul Scherrer Institute (PSI) based on the best-estimate coupled neutronic/thermal–hydraulics code, SIMULATE-3K (S3K). For each new stability investigation, the concept is to apply a systematic methodology, combining a single unique S3K vessel T/H model with a full 3-D core model directly transferred from the upstream validated core model, without any adjustments of neither circulation loop components nor fuel assembly geometries/characteristics nor calculation options (e.g. physical models). Through this, the aim is to achieve an integral methodology that can then be applied with strengthened reliability for predictions and/or interpretations of the complex non-linear and strongly coupled neutronics/dynamical phenomena characterizing BWR stability However, the methodology has so far not been validated for regional instabilities and to that aim, a special KKL cycle 07 stability test was selected. Indeed, during this test, the core not only showed growing power oscillation amplitudes in an out-of-phase regime but also an oscillating and rotating symmetry line. Thereby, it was considered highly appropriate to start the validation of the PSI S3K methodology for regional instabilities using this particular test and to gain, on that basis, more insights on the causes for oscillatory and rotational behavior of symmetry lines. The results obtained so far are presented in this paper. First, it is found that the S3K results are in good agreement with measurements both qualitatively and quantitatively, although the resonance frequency is slightly over-predicted. Secondly, the excitation of the out-of-phase mode with oscillation as well as rotation of the symmetry line is also well captured in full accordance with the experimental observations. Related to this, an in-depth analysis of LPRM signals indicates that two out-of-phase oscillation modes associated to two azimuthal neutronic modes are simultaneously excited. Furthermore, it is found that a superposition of these two modes with non-zero phase shift will trigger the symmetry line dynamics and that the behavior will be guided by the dominance ratio between these two modes. More precisely, the oscillatory behavior is due to the superposition of the two azimuthal modes but with one dominant mode. The rotational behavior is however due to the superposition of the two modes with comparable strengths. Moreover, out-of-phase higher mode oscillations are also predicted, showing time-frames when the core is divided into four and even six regions with each region oscillating out-of-phase with respect to its adjacent region. Finally, a bifurcation analysis shows that the observed limit cycle is associated to the occurrence of a supercritical Hopf bifurcation.