STABILITY ANALYSIS OF BWR NUCLEAR-COUPLED THERMAL-HYDRAULICS USING A SIMPLE-MODEL

A simple mathematical model is developed to describe the dynamics of t he nuclear-coupled thermal-hydraulics in a boiling water reactor (BWR) core. The model, which incorporates the essential features of neutron kinetics and single-phase and two-phase thermal-hydraulics, leads to a simple dynamical system comprised of a set of nonlinear ordinary dif ferential equations (ODEs). The stability boundary is determined and p lotted in the inlet-subcooling-number (enthalpy)/external-reactivity o perating parameter plane. The eigenvalues of the Jacobian matrix of th e dynamical system also are calculated at various steady-states (fixed points); the results are consistent with those of the direct stabilit y analysis and indicate that a Hopf bifurcation occurs as the stabilit y boundary in the operating parameter plane is crossed. Numerical simu lations of the time-dependent, nonlinear ODEs are carried out for sele cted points in the operating parameter plane to obtain the actual damp ed and growing oscillations in the neutron number density, the channel inlet flow velocity, and the other phase variables. These indicate th at the Hopf bifurcation is subcritical, hence, density wave oscillatio ns with growing amplitude could result from a finite perturbation of t he system even when it is being operated in the parameter region thoug ht to be safe, i.e. where the steady-state is stable. Finally, the pow er-flow map, frequently used by reactor operators during start-up and shut-down operation of a BWR, is mapped to the inlet-subcooling-number /neutron-density (operating-parameter/phase-variable) plane, and then related to the stability boundaries for different fixed inlet velociti es corresponding to selected points on the flow-control line. Also, th e stability boundaries for different fixed inlet subcooling numbers co rresponding to those selected points, are plotted in the neutron-densi ty/inlet-velocity phase variable plane and then the points on the flow -control line are related to their respective stability boundaries in this plane. The relationship of the operating points on the flow-contr ol line to their respective stability boundaries in these two planes p rovides insight into the instability observed in BWRs during low-flow/ high-power operating conditions. It also shows that the normal operati ng point of a BWR is very stable in comparison with other possible ope rating points on the power-flow map. (C) 1997 Elsevier Science S.A.