Nonlinear analysis of a natural circulation boiling water reactor

A dynamic model of natural circulation boiling water reactors (BWRs) is analyzed using a bifurcation code and numerical simulations. The two fundamental bifurcation types relevant to BWRs, the supercritical and the subcritical Hopf bifurcations, are first studied in natural circulation systems without nuclear feedback. The effect of nodalization approximation in the riser on stability and bifurcation characteristics of the system is determined. The strong effect of the nuclear-thermohydraulic interaction on the nonlinear characteristics of a natural circulation BWR is then explored in a parametric study. Supercritical bifurcations become dominant in the (high-power) Type-II region for small values of the subcooling number and a strong nuclear-thermohydraulic coupling. A cascade of period-doubling pitchfork bifurcations (deep in the unstable region) is also predicted by the model under these conditions. Subcritical bifurcations in the Type-II instability region were found for larger values of the subcooling number. Both Hopf-bifurcation modes were also encountered in the Type-I instability region (low power or high power/ high subcooling). Finally, the nonlinear reactor model was validated successfully compared with nonlinear power oscillations measured in a natural circulation BWR.