Turning points and sub- and supercritical bifurcations in a simple BWR model

Abstract

Stability and semi-analytical bifurcation analyses of BWRs have been performed using a dynamical system approach. A reduced order model of a BWR that includes simple neutronics as well as thermal hydraulics has been used. Analyses have been carried out using a bifurcation analysis code, BIFDD, that carries out analytic–numeric stability and bifurcation analyses of set of ordinary differential equations and ODEs with delays. A large segment of the parameter space has been investigated using this very efficient tool. Stability boundaries are obtained in several two-dimensional parameter spaces. In addition, the nature of bifurcation along these stability boundaries has also been determined. Results indicate that both subcritical as well as supercritical Poincaré–Andronov–Hopf bifurcations are likely to occur in regions of interest in parameter space. In addition to the semi-analytical bifurcation studies, the governing equations have also been integrated numerically. Results confirm the findings of the stability and bifurcation analyses. Numerical integrations, carried out for parameter values away from the stability boundary, further show that the bifurcation curves, in many cases of subcritical bifurcations, have a turning point. The bifurcation curve in these cases extends back into the unstable region. These results show that it is possible to experience large amplitude stable oscillations in the unstable region infinitesimally close to the stability boundary. Moreover, large amplitude stable oscillations are also possible, following large but finite perturbations, in the stable region of the parameter space near the stability boundary. These findings provide alternate explanation for the experimental and operational observations in BWRs that indicate the existence of stable limit cycle oscillations and the possibility of growing amplitude oscillations. Results obtained here using a simple model suggest that further work along these lines, with more detailed models, is needed to identify operating conditions and perturbation amplitudes that might lead to stable limit cycles or growing amplitude oscillations in current and next generation of BWRs.