Singular Perturbation Analysis of Limit Cycle Behavior in Nuclear-Coupled Density-Wave Oscillations

An investigation of the potential behavior of large amplitude nuclear-coupled density-wave oscillations in a boiling water reactor (BWR) was performed. A simplified, nonlinear BWR core model was developed and used to predict the growth of oscillations as a limit cycle is approached. For high-power/low-flow initial conditions, large density-wave oscillations could cause periodic pulses in core power. The fuel temperature, which rapidly increases at high-power conditions and slowly recovers, is considered as the fast variable in a relaxation oscillation. With an appropriate transformation of the system equations, the approximate limit cycle trajectory can therefore be determined using singular perturbation analysis. In the first approximation, where the relaxation is assumed to occur infinitely fast, the phase-space trajectory combines the slow part with an instantaneous jump between end points to form a closed cycle. The accuracy of this approximation is improved with appropriate perturbation series expansions on both the slow and fast parts, as well as introduction of a separate expansion for the connections between these parts. The approximate solution is considerably simpler to obtain than a conventional numerical solution of the original equations.