Nonlinear stability analysis of a reduced order model of nuclear reactors: A parametric study relevant to the advanced heavy water reactor

In this paper, we perform a parametric study of the nonlinear dynamics of a reduced order model for boiling water reactors (BWR) near the Hopf bifurcation point using the method of multiple scales (MMS). Analysis has been performed for general values of the parameters, but the results are demonstrated for parameter values of the model corresponding to the advanced heavy water reactor (AHWR). The neutronics of the AHWR is modeled using point reactor kinetic equations while a one-node lumped parameter model is assumed both for the fuel and the coolant for modeling the thermal-hydraulics. Nonlinearities in the heat transfer process are ignored and attention is focused on the nonlinearity introduced by the reactivity feedback. It is found that the steady-state operation of the AHWR mathematical model looses stability via. a Hopf bifurcation resulting in power oscillations as some typical bifurcation parameter like the void coefficient of reactivity is varied. The bifurcation is found to be subcritical for the parameter values corresponding to the AHWR. However, with a decrease in the fuel temperature coefficient of reactivity the bifurcation turns to supercritical implying global stability of the steady state operation in the linear stability regime. Moreover slight intrusion into the instability regime results in small-amplitude limit cycles leaving the possibility of retracting back to stable operation.