| We have studied the nuclear-coupled thermal-hydraulic stability of boiling water reactors (BWRs) using a model we developed from: the space-time modal neutron kinetics equations based on spatial ;We first determine the stability boundary (SB) in the most relevant parameter plane, the inlet-subcooling-number/external-pressure-drop plane, for a fixed control rod induced external reactivity equal to the 100% rod line value and then transform the SB to the practical power-flow map. Using this SB, we show that the normal operating point at 100% power is very stable, stability of points on the 100% rod line decreases as the flow rate is reduced, and that points are least stable in the low-flow/high-power region. We also determine the SB when the modal kinetics is replaced by simple point reactor kinetics and show that the first harmonic mode has no significant effect on the SB.;Later we carry out the relevant numerical simulations where we first show that the Hopf bifurcation, that occurs as a parameter is varied across the SB is subcritical, and that, in the important low-flow/high-power region, growing oscillations can result following small finite perturbations of stable steady-states on the 100% rod line. Hence, a point on the 100% rod line in the low-flow/high-power region, although stable, may nevertheless be a point at which a BWR should not be operated. Numerical simulations are then done to calculate the decay ratios (DRs) and frequencies of oscillations for various points on the 100% rod line. It is determined that the NRC requirement of DR ;Finally, the effect of a simple recirculation loop model that we develop is studied by carrying out additional stability analyses and additional numerical simulations. It is shown that the loop has a stabilizing effect on certain points on the 100% rod line for time delays equal to integer multiples of the natural period of oscillation, whereas it has a destabilizing effect for half-integer multiples. However, for more practical time delays, it is determined that the overall effect generally is destabilizing. |
