Detailed bifurcation analysis with a simplified model for advance heavy water reactor system

The bifurcation analysis of fixed points and limit cycles with a simplified mathematical model representing system dynamics of a boiling water reactor has been carried out, specifically parameter values for AHWR is used. The lumped parameter model that includes point reactor kinetics equation for neutron balance in the reactor core and one node model for fuel and coolant thermal hydraulics is used in the analysis. The nonlinearity due to reactivity is considered in the present model; while other nonlinearities due to heat transfer process between fuel–clad and fuel–coolant has been neglected. The system loses its stability via Hopf bifurcation as the system parameters are varied. The continuations of subcritical and supercritical Hopf points show the existence of limit point bifurcations of limit cycles (LPC). The codimension one and codimension two bifurcations of fixed points for the system have been analyzed. The stability of observed limit cycles has been analyzed by Floquet multiplier as well as by Lyapunov coefficient. The pattern of limit cycles and envelopes of limit cycles over the fixed points have been studied by numerical integrations and depicted by time history graphs.